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Weighted estimates for product singular integral operators in Journé’s class on RD-spaces Forum Math. (IF 0.8) Pub Date : 2024-04-17 Taotao Zheng, Yanmei Xiao, Xiangxing Tao
An RD-space 𝑀 is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in 𝑀. In this paper, firstly, the authors give the Plancherel–Pôlya characterization of product weighted Triebel–Lizorkin spaces and product weighted Besov spaces on RD-spaces and make some estimates for the product singular integral operators in Journé’s
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Colored multizeta values in positive characteristic Forum Math. (IF 0.8) Pub Date : 2024-04-04 Ryotaro Harada
In 2004, Thakur introduced a positive characteristic analogue of multizeta values. Later, in 2017, he mentioned the two colored variants which are positive characteristic analogues of colored multizeta values in his survey of multizeta values in positive characteristic. In this paper, we study one of those two variants. We establish their fundamental properties, that include their non-vanishing, sum-shuffle
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On projections of the tails of a power Forum Math. (IF 0.8) Pub Date : 2024-04-03 Samuel M. Corson, Saharon Shelah
Let 𝜅 be an inaccessible cardinal, 𝔘 a universal algebra, and ∼ \sim the equivalence relation on U κ \mathfrak{U}^{\kappa} of eventual equality. From mild assumptions on 𝜅, we give general constructions of E ∈ End ( U κ / ∼ ) \mathcal{E}\in\operatorname{End}(\mathfrak{U}^{\kappa}/{\sim}) satisfying E ∘ E = E \mathcal{E}\circ\mathcal{E}=\mathcal{E} which do not descend from Δ ∈ End ( U κ ) \De
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Free groups generated by two unipotent maps Forum Math. (IF 0.8) Pub Date : 2024-03-25 Chao Jiang, Baohua Xie
Let A and B be two unipotent elements of SU ( 2 , 1 ) {\mathrm{SU}(2,1)} with distinct fixed points. In [S. B. Kalane and J. R. Parker, Free groups generated by two parabolic maps, Math. Z. 303 2023, 1, Paper No. 9], the authors gave several conditions that guarantee the subgroup 〈 A , B 〉 {\langle A,B\rangle} is discrete and free by using Klein’s combination theorem. We will improve their conditions
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On the Iwasawa main conjecture for generalized Heegner classes in a quaternionic setting Forum Math. (IF 0.8) Pub Date : 2024-03-25 Maria Rosaria Pati
We prove one divisibility relation of the anticyclotomic Iwasawa Main Conjecture for a higher weight ordinary modular form f and an imaginary quadratic field satisfying a “relaxed” Heegner hypothesis. Let Λ be the anticyclotomic Iwasawa algebra. Following the approach of Howard and Longo–Vigni, we construct the Λ-adic Kolyvagin system of generalized Heegner classes coming from Heegner points on a suitable
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Paley inequality for the Weyl transform and its applications Forum Math. (IF 0.8) Pub Date : 2024-03-25 Ritika Singhal, N. Shravan Kumar
In this paper, we prove several versions of the classical Paley inequality for the Weyl transform. As for some applications, we prove a version of the Hörmander’s multiplier theorem to discuss L p {L^{p}} - L q {L^{q}} boundedness of the Weyl multipliers and prove the Hardy–Littlewood inequality. We also consider the vector-valued version of the inequalities of Paley, Hausdorff–Young, and Hardy–Littlewood
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On arithmetic quotients of the group SL2 over a quaternion division k-algebra Forum Math. (IF 0.8) Pub Date : 2024-03-25 Sophie Koch, Joachim Schwermer
Given a totally real algebraic number field k of degree s, we consider locally symmetric spaces X G / Γ {X_{G}/\Gamma} associated with arithmetic subgroups Γ of the special linear algebraic k-group G = SL M 2 ( D ) {G=\mathrm{SL}_{M_{2}(D)}} , attached to a quaternion division k-algebra D. The group G is k-simple, of k-rank one, and non-split over k. Using reduction theory, one can construct an open
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Existence and multiplicity of solutions for fractional Schrödinger-p-Kirchhoff equations in ℝ N Forum Math. (IF 0.8) Pub Date : 2024-03-25 Huo Tao, Lin Li, Patrick Winkert
This paper concerns the existence and multiplicity of solutions for a nonlinear Schrödinger–Kirchhoff-type equation involving the fractional p-Laplace operator in ℝ N {\mathbb{R}^{N}} . Precisely, we study the Kirchhoff-type problem ( a + b ∬ ℝ 2 N | u ( x ) - u ( y ) | p | x - y | N + s p d x d y ) ( - Δ ) p s u + V ( x ) | u | p - 2 u = f ( x , u ) in ℝ N , \Biggl{(}a
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A Kollár-type vanishing theorem for k-positive vector bundles Forum Math. (IF 0.8) Pub Date : 2024-03-25 Chen Zhao
Given a proper holomorphic surjective morphism f : X → Y {f:X\rightarrow Y} between compact Kähler manifolds, and a Nakano semipositive holomorphic vector bundle E on X, we prove Kollár-type vanishing theorems on cohomologies with coefficients in R q f ∗ ( ω X ( E ) ) ⊗ F {R^{q}f_{\ast}(\omega_{X}(E))\otimes F} , where F is a k-positive vector bundle on Y. The main inputs in the proof are the
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Triangles with one fixed side–length, a Furstenberg-type problem, and incidences in finite vector spaces Forum Math. (IF 0.8) Pub Date : 2024-03-25 Thang Pham
The first goal of this paper is to prove a sharp condition to guarantee of having a positive proportion of all congruence classes of triangles in given sets in 𝔽 q 2 {\mathbb{F}_{q}^{2}} . More precisely, for A , B , C ⊂ 𝔽 q 2 {A,B,C\subset\mathbb{F}_{q}^{2}} , if | A | | B | | C | 1 2 ≫ q 4 {|A||B||C|^{\frac{1}{2}}\gg q^{4}} , then for any λ ∈ 𝔽 q ∖ { 0 } {\lambda\in\mathbb{F}_{q}\setminus\{0\}}
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Existence of strong solutions for one-dimensional reflected mixed stochastic delay differential equations Forum Math. (IF 0.8) Pub Date : 2024-03-25 Monir Chadad, Mohamed Erraoui
Relying on the pathwise uniqueness property, we prove existence of the strong solution of a one-dimensional reflected stochastic delay equation driven by a mixture of independent Brownian and fractional Brownian motions. The difficulty is that on the one hand we cannot use the fixed-point and contraction mapping methods because of the stochastic and pathwise integrals, and on the other hand the non-continuity
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Simultaneous nonvanishing of central L-values with large level Forum Math. (IF 0.8) Pub Date : 2024-03-25 Balesh Kumar, Murugesan Manickam, Karam Deo Shankhadhar
For a given normalized newform f of large prime level, we establish a lower bound with respect to the level for the number of normalized newforms g of the same weight and level as of f such that the central L-values of f and g both twisted by a quadratic character do not vanish.
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Euler’s integral, multiple cosine function and zeta values Forum Math. (IF 0.8) Pub Date : 2024-03-25 Su Hu, Min-Soo Kim
In 1769, Euler proved the following result: ∫ 0 π 2 log ( sin θ ) 𝑑 θ = - π 2 log 2 . \int_{0}^{\frac{\pi}{2}}\log(\sin\theta)\,d\theta=-\frac{\pi}{2}\log 2. In this paper, as a generalization, we evaluate the definite integrals ∫ 0 x θ r - 2 log ( cos θ 2 ) 𝑑 θ \int_{0}^{x}\theta^{r-2}\log\biggl{(}\cos\frac{\theta}{2}\biggr{)}\,d\theta for r = 2 , 3 , 4 , … r=2,3,4,\dots . We show
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Arithmetic progression in a finite field with prescribed norms Forum Math. (IF 0.8) Pub Date : 2024-03-25 Kaustav Chatterjee, Hariom Sharma, Aastha Shukla, Shailesh Kumar Tiwari
Given a prime power q and a positive integer n, let 𝔽 q n {\mathbb{F}_{q^{n}}} represent a finite extension of degree n of the finite field 𝔽 q {{\mathbb{F}_{q}}} . In this article, we investigate the existence of m elements in arithmetic progression, where every element is primitive and at least one is normal with prescribed norms. Moreover, for n ≥ 6 {n\geq 6} , q = 3 k {q=3^{k}} , m = 2 {m=2}
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The existence of optimal solutions for nonlocal partial systems involving fractional Laplace operator with arbitrary growth Forum Math. (IF 0.8) Pub Date : 2024-03-25 Siyao Peng
In this paper, we investigate nonlocal partial systems that incorporate the fractional Laplace operator. Our primary focus is to establish a theorem concerning the existence of optimal solutions for these equations. To achieve this, we utilize two fundamental tools: information obtained from an iterative reconstruction algorithm and a variant of the Phragmén–Lindelöf principle of concentration and
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Some q-supercongruences from a q-analogue of Watson's 3 F 2 summation Forum Math. (IF 0.8) Pub Date : 2024-03-25 Victor J. W. Guo
We give some q-supercongruences from a q-analogue of Watson’s F 2 3 {{}_{3}F_{2}} summation and the method of “creative microscoping”, introduced by the author and Zudilin. These q-supercongruences may be considered as further generalizations of the (A.2) supercongruence of Van Hamme modulo p 3 {p^{3}} or p 2 {p^{2}} for any odd prime p. Meanwhile, we confirm a supercongruence conjecture of Wang and
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Estimates of Picard modular cusp forms Forum Math. (IF 0.8) Pub Date : 2024-03-25 Anilatmaja Aryasomayajula, Baskar Balasubramanyam, Dyuti Roy
In this article, for n ≥ 2 {n\geq 2} , we compute asymptotic, qualitative, and quantitative estimates of the Bergman kernel of Picard modular cusp forms associated to torsion-free, cocompact subgroups of SU ( ( n , 1 ) , ℂ ) {\mathrm{SU}((n,1),\mathbb{C})} . The main result of the article is the following result. Let Γ ⊂ SU ( ( 2 , 1 ) , 𝒪 K ) {\Gamma\subset\mathrm{SU}((2,1),\mathcal{O}_{K})}
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Explicit bounds for the solutions of superelliptic equations over number fields Forum Math. (IF 0.8) Pub Date : 2024-03-25 Attila Bérczes, Yann Bugeaud, Kálmán Győry, Jorge Mello, Alina Ostafe, Min Sha
Let f be a polynomial with coefficients in the ring O S {O_{S}} of S-integers of a number field K, b a non-zero S-integer, and m an integer ≥ 2 {\geq 2} . We consider the following equation ( ⋆ ) {(\star)} : f ( x ) = b y m {f(x)=by^{m}} in x , y ∈ O S {x,y\in O_{S}} . Under the well-known LeVeque condition, we give fully explicit upper bounds in terms of K , S , f , m {K,S,f,m} and the S-norm
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A p-adic analog of Hasse--Davenport product relation involving ϵ-factors Forum Math. (IF 0.8) Pub Date : 2024-03-25 Dani Szpruch
In this paper we prove some generalizations of the classical Hasse–Davenport product relation for certain arithmetic factors defined on a p-adic field F, among them one finds the ϵ-factors appearing in Tate’s thesis. We then show that these generalizations are equivalent to some representation theoretic identities relating the determinant of ramified local coefficients matrices defined for coverings
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Degenerate Schrödinger--Kirchhoff {(p,N)}-Laplacian problem with singular Trudinger--Moser nonlinearity in ℝ N Forum Math. (IF 0.8) Pub Date : 2024-03-25 Deepak Kumar Mahanta, Tuhina Mukherjee, Abhishek Sarkar
In this paper, we deal with the existence of nontrivial nonnegative solutions for a ( p , N ) {(p,N)} -Laplacian Schrödinger–Kirchhoff problem in ℝ N {\mathbb{R}^{N}} with singular exponential nonlinearity. The main features of the paper are the ( p , N ) {(p,N)} growth of the elliptic operators, the double lack of compactness, and the fact that the Kirchhoff function is of degenerate type. To establish
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Homogeneous ACM and Ulrich bundles on rational homogeneous spaces Forum Math. (IF 0.8) Pub Date : 2024-03-22 Xinyi Fang
In this paper, we characterize homogeneous arithmetically Cohen–Macaulay (ACM) bundles and Ulrich bundles on rational homogeneous spaces. From this result, we see that there are only finitely many irreducible homogeneous ACM bundles (up to twist) and Ulrich bundles on these varieties. Moreover, we give numerical criteria for some special irreducible homogeneous bundles to be ACM bundles.
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New sequence spaces derived by using generalized arithmetic divisor sum function and compact operators Forum Math. (IF 0.8) Pub Date : 2024-03-04 Taja Yaying, Nipen Saikia, Mohammad Mursaleen
Define an infinite matrix D α = ( d n , v α ) \mathfrak{D}^{\alpha}=(d^{\alpha}_{n,v}) by d n , v α = { v α σ ( α ) ( n ) , v ∣ n , 0 , v ∤ n , d^{\alpha}_{n,v}=\begin{cases}\dfrac{v^{\alpha}}{\sigma^{(\alpha)}(n)},&v\mid n,\\ 0,&v\nmid n,\end{cases} where σ ( α ) ( n ) \sigma^{(\alpha)}(n) is defined to be the sum of the 𝛼-th power of the positive divisors of n ∈ N n\in\mathbb{N} , and construct
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Building planar polygon spaces from the projective braid arrangement Forum Math. (IF 0.8) Pub Date : 2024-02-28 Navnath Daundkar, Priyavrat Deshpande
The moduli space of planar polygons with generic side lengths is a smooth, closed manifold. It is known that these manifolds contain the moduli space of distinct points on the real projective line as an open dense subset. Kapranov showed that the real points of the Deligne–Mumford–Knudson compactification can be obtained from the projective Coxeter complex of type 𝐴 (equivalently, the projective braid
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q-supercongruences from Watson's 8φ7 transformation Forum Math. (IF 0.8) Pub Date : 2024-02-20 Xiaoxia Wang, Chang Xu
Employing Watson’s ϕ 7 8 {{}_{8}\phi_{7}} transformation formula, we unearth several q-supercongruences with a parameter s. Particularly, one of our results is an extension of a q-analogue of Van Hamme’s (G.2) supercongruence. In addition, we obtain a q-supercongruence modulo the fifth power of a cyclotomic polynomial and propose two related conjectures.
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Uniform bounds for Kloosterman sums of half-integral weight with applications Forum Math. (IF 0.8) Pub Date : 2024-02-20 Qihang Sun
Sums of Kloosterman sums have deep connections with the theory of modular forms, and their estimation has many important consequences. Kuznetsov used his famous trace formula and got a power-saving estimate with respect to x with implied constants depending on m and n. Recently, in 2009, Sarnak and Tsimerman obtained a bound uniformly in x, m and n. The generalized Kloosterman sums are defined with
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Orthogonal separation of variables for spaces of constant curvature Forum Math. (IF 0.8) Pub Date : 2024-02-20 Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
We construct all orthogonal separating coordinates in constant curvature spaces of arbitrary signature. Further, we construct explicit transformation between orthogonal separating and flat or generalised flat coordinates, as well as explicit formulas for the corresponding Killing tensors and Stäckel matrices.
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Joint distribution of the cokernels of random p-adic matrices II Forum Math. (IF 0.8) Pub Date : 2024-02-20 Jiwan Jung, Jungin Lee
In this paper, we study the combinatorial relations between the cokernels cok ( A n + p x i I n ) {\operatorname{cok}(A_{n}+px_{i}I_{n})} ( 1 ≤ i ≤ m {1\leq i\leq m} ), where A n {A_{n}} is an n × n {n\times n} matrix over the ring of p-adic integers ℤ p {\mathbb{Z}_{p}} , I n {I_{n}} is the n × n {n\times n} identity matrix and x 1 , … , x m {x_{1},\dots,x_{m}} are elements of ℤ p {\mathbb{Z}_{p}}
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Fundamental properties of Cauchy–Szegő projection on quaternionic Siegel upper half space and applications Forum Math. (IF 0.8) Pub Date : 2024-02-20 Der-Chen Chang, Xuan Thinh Duong, Ji Li, Wei Wang, Qingyan Wu
We investigate the Cauchy–Szegő projection for quaternionic Siegel upper half space to obtain the pointwise (higher order) regularity estimates for Cauchy–Szegő kernel and prove that the Cauchy–Szegő kernel is nonzero everywhere, which further yields a non-degenerated pointwise lower bound. As applications, we prove the uniform boundedness of Cauchy–Szegő projection on every atom on the quaternionic
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Some properties of extended frame measure Forum Math. (IF 0.8) Pub Date : 2024-02-20 Jinjun Li, Zhiyi Wu, Fusheng Xiao
We prove that the extended frame spectral measures are of pure type and the Beurling dimension of any frame measure for an extended frame spectral measure is in its Fourier dimension and upper entropy dimension.
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Submodules of normalisers in groupoid C*-algebras and discrete group coactions Forum Math. (IF 0.8) Pub Date : 2024-02-20 Fuyuta Komura
In this paper, we investigate certain submodules in C*-algebras associated to effective étale groupoids. First, we show that a submodule generated by normalizers is a closure of the set of compactly supported continuous functions on some open set. As a corollary, we show that discrete group coactions on groupoid C*-algebras are induced by cocycles of étale groupoids if the fixed point algebras contain
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Normalized solutions for the fractional Schrödinger equation with combined nonlinearities Forum Math. (IF 0.8) Pub Date : 2024-01-31 Shengbing Deng, Qiaoran Wu
In this paper, we study the normalized solutions for the following fractional Schrödinger equation with combined nonlinearities { ( - Δ ) s u = λ u + μ | u | q - 2 u + | u | p - 2 u in ℝ N , ∫ ℝ N u 2 𝑑 x = a 2 , \displaystyle\left\{\begin{aligned} \displaystyle{}(-\Delta)^{s}u&% \displaystyle=\lambda u+\mu\lvert u\rvert^{q-2}u+\lvert u\rvert^{p-2}u&&% \displaystyle\phantom{}\text{in
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The C*-algebra of the Boidol group Forum Math. (IF 0.8) Pub Date : 2024-01-31 Ying-Fen Lin, Jean Ludwig
The Boidol group is the smallest non- ∗ {\ast} -regular exponential Lie group. It is of dimension 4 and its Lie algebra is an extension of the Heisenberg Lie algebra by the reals with the roots 1 and -1. We describe the C*-algebra of the Boidol group as an algebra of operator fields defined over the spectrum of the group. It is the only connected solvable Lie group of dimension less than or equal to
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Cellular covers of divisible uniserial modules over valuation domains Forum Math. (IF 0.8) Pub Date : 2024-01-31 László Fuchs, Brendan Goldsmith, Luigi Salce, Lutz Strüngmann
Cellular covers which originate in homotopy theory are considered here for a very special class: divisible uniserial modules over valuation domains. This is a continuation of the study of cellular covers of divisible objects, but in order to obtain more substantial results, we are restricting our attention further to specific covers or to specific kernels. In particular, for h-divisible uniserial modules
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Profinite genus of fundamental groups of compact flat manifolds with the cyclic holonomy group of square-free order Forum Math. (IF 0.8) Pub Date : 2024-01-31 Genildo de Jesus Nery
In this article, we study the extent to which an n-dimensional compact flat manifold with the cyclic holonomy group of square-free order may be distinguished by the finite quotients of its fundamental group. In particular, we display a formula for the cardinality of profinite genus of the fundamental group of an n-dimensional compact flat manifold with the cyclic holonomy group of square-free order
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Degrees of generalized Kloosterman sums Forum Math. (IF 0.8) Pub Date : 2024-01-30 Liping Yang
The modern study of the exponential sums is mainly about their analytic estimates as complex numbers, which is local. In this paper, we study one global property of the exponential sums by viewing them as algebraic integers. For a kind of generalized Kloosterman sums, we present their degrees as algebraic integers.
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Bi-parameter and bilinear Calderón–Vaillancourt theorem with critical order Forum Math. (IF 0.8) Pub Date : 2024-01-30 Jiao Chen, Liang Huang, Guozhen Lu
In this paper, we establish the sharp Calderón–Vaillancourt theorem on L p L^{p} spaces for bi-parameter and bilinear pseudo-differential operators with symbols of critical order by deriving a sufficient and necessary condition on its symbol. This sharpens the result of [G. Lu and L. Zhang, Bi-parameter and bilinear Calderón–Vaillancourt theorem with subcritical order, Forum Math. 28 2016, 6, 1087–1094]
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Algebraic results on rngs of singular functions Forum Math. (IF 0.8) Pub Date : 2024-01-30 Arran Fernandez, Müge Saadetoğlu
We consider a Mikusiński-type convolution algebra C α {C_{\alpha}} , including functions with power-type singularities at the origin as well as all functions continuous on [ 0 , ∞ ) {[0,\infty)} . Algebraic properties of this space are derived, including its ideal structure, filtered and graded structure, and Jacobson radical. Applications to operators of fractional calculus and the associated integro-differential
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Hardy inequalities on metric measure spaces, IV: The case p=1 Forum Math. (IF 0.8) Pub Date : 2024-01-14 Michael Ruzhansky, Anjali Shriwastawa, Bankteshwar Tiwari
In this paper, we investigate the two-weight Hardy inequalities on metric measure space possessing polar decompositions for the case p = 1 {p=1} and 1 ≤ q < ∞ {1\leq q<\infty} . This result complements the Hardy inequalities obtained in [M. Ruzhansky and D. Verma, Hardy inequalities on metric measure spaces, Proc. Roy. Soc. A. 475 2019, 2223, Article ID 20180310] in the case 1 < p ≤ q < ∞ {1 1 {p>1}
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Transcendence on algebraic groups Forum Math. (IF 0.8) Pub Date : 2024-01-10 Duc Hiep Pham
In this paper, we give some new results on transcendence on algebraic groups. These results extend some previous ones established on commutative or linear algebraic groups to arbitrary algebraic groups in complex and p-adic fields, respectively.
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Supercongruences arising from a 7 F 6 hypergeometric transformation formula Forum Math. (IF 0.8) Pub Date : 2024-01-10 Chen Wang
Using a F 6 7 {{}_{7}F_{6}} hypergeometric transformation formula, we prove two supercongruences. In particular, one of these supercongruences confirms a recent conjecture of Guo, Liu and Schlosser, and gives an extension of a supercongruence of Long and Ramakrishna.
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An explicit version of Bombieri’s log-free density estimate and Sárközy’s theorem for shifted primes Forum Math. (IF 0.8) Pub Date : 2024-01-10 Jesse Thorner, Asif Zaman
We make explicit Bombieri’s refinement of Gallagher’s log-free “large sieve density estimate near σ = 1 {\sigma=1} ” for Dirichlet L-functions. We use this estimate and recent work of Green to prove that if N ≥ 2 {N\geq 2} is an integer, A ⊆ { 1 , … , N } {A\subseteq\{1,\ldots,N\}} , and for all primes p no two elements in A differ by p - 1 {p-1} , then | A | ≪ N 1 - 10 - 18 {|A|\ll N^{1-10^{-18}}}
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Multiple normalized solutions for fractional elliptic problems Forum Math. (IF 0.8) Pub Date : 2024-01-10 Thin Van Nguyen, Vicenţiu D. Rădulescu
In this article, we are first concerned with the existence of multiple normalized solutions to the following fractional p-Laplace problem: { ( - Δ ) p s v + 𝒱 ( ξ x ) | v | p - 2 v = λ | v | p - 2 v + f ( v ) in ℝ N , ∫ ℝ N | v | p 𝑑 x = a p , \left\{\begin{aligned} \displaystyle{}(-\Delta)_{p}^{s}v+\mathcal{V}(\xi x)% \lvert v\rvert^{p-2}v&\displaystyle=\lambda\lvert v\rvert^{p-2}v+f(v)\quad%
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Topological amenability of semihypergroups Forum Math. (IF 0.8) Pub Date : 2024-01-05 Choiti Bandyopadhyay
In this article, we introduce and explore the notion of topological amenability in the broad setting of (locally compact) semihypergroups. We acquire several stationary, ergodic and Banach algebraic characterizations of the same in terms of convergence of certain probability measures, total variation of convolution with probability measures and translation of certain functionals, as well as the F-algebraic
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What conjugate phase retrieval complex vectors can do in quaternion Euclidean spaces Forum Math. (IF 0.8) Pub Date : 2024-01-05 Yun-Zhang Li, Ming Yang
Quaternion algebra ℍ {\mathbb{H}} is a noncommutative associative algebra. In recent years, quaternionic Fourier analysis has received increasing attention due to its applications in signal analysis and image processing. This paper addresses conjugate phase retrieval problem in the quaternion Euclidean space ℍ M {\mathbb{H}^{M}} with M ≥ 2 {M\geq 2} . Write ℂ η = { ξ : ξ = ξ 0 + β η , ξ 0 , β ∈ ℝ
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Wells-type exact sequence and crossed extensions of algebras with bracket Forum Math. (IF 0.8) Pub Date : 2024-01-05 José Manuel Casas, Emzar Khmaladze, Manuel Ladra
We study the extensibility problem of a pair of derivations associated with an abelian extension of algebras with bracket, and derive an exact sequence of the Wells type. We introduce crossed modules for algebras with bracket and prove their equivalence with internal categories in the category of algebras with bracket. We interpret the set of equivalence classes of crossed extensions as the second
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Topological embeddings into transformation monoids Forum Math. (IF 0.8) Pub Date : 2024-01-05 Serhii Bardyla, Luke Elliott, James D. Mitchell, Yann Péresse
In this paper we consider the questions of which topological semigroups embed topologically into the full transformation monoid ℕ ℕ {\mathbb{N}^{\mathbb{N}}} or the symmetric inverse monoid I ℕ {I_{\mathbb{N}}} with their respective canonical Polish semigroup topologies. We characterise those topological semigroups that embed topologically into ℕ ℕ {\mathbb{N}^{\mathbb{N}}} and belong to any of the
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Multilinear Fourier integral operators on modulation spaces Forum Math. (IF 0.8) Pub Date : 2024-01-04 Aparajita Dasgupta, Lalit Mohan, Shyam Swarup Mondal
In this article, we study properties of multilinear Fourier integral operators on weighted modulation spaces. In particular, using the theory of Gabor frames, we study boundedness of multilinear Fourier integral operators on products of weighted modulation spaces. Further, we investigate the periodic multilinear Fourier integral operator. Finally, we study continuity of bilinear pseudo-differential
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Archimedean toroidal maps and their edge covers Forum Math. (IF 0.8) Pub Date : 2024-01-01 Arnab Kundu, Dipendu Maity
The automorphism group of a map on a surface acts naturally on its flags (triples of incident vertices, edges, and faces). We will study the action of the automorphism group of a map on its edges. A map is semi-equivelar if all of its vertices have the same type of face-cycles. A semi-equivelar toroidal map refers to a semi-equivelar map embedded on a torus. If a map has k edge orbits under its automorphism
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Finite approximation properties of C*-modules III Forum Math. (IF 0.8) Pub Date : 2024-01-01 Massoud Amini
We introduce and study a notion of module nuclear dimension for a C * \mathrm{C}^{*} -algebra A which is a C * \mathrm{C}^{*} -module over another C * \mathrm{C}^{*} -algebra 𝔄 {\mathfrak{A}} with compatible actions. We show that the module nuclear dimension of A is zero if A is 𝔄 {\mathfrak{A}} -NF. The converse is shown to hold when 𝔄 {\mathfrak{A}} is a C ( X ) {C(X)} -algebra with simple fibers
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Tilings of the sphere by congruent quadrilaterals III: Edge combination a 3 b with general angles Forum Math. (IF 0.8) Pub Date : 2024-01-01 Yixi Liao, Pinren Qian, Erxiao Wang, Yingyun Xu
Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This last one classifies the case of a 3 b {a^{3}b} -quadrilaterals with some irrational angle: there are a sequence of 1-parameter families of quadrilaterals admitting 2-layer earth map tilings together with their basic flip modifications under extra condition, and 5 sporadic quadrilaterals
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On the modular isomorphism problem for groups of nilpotency class 2 with cyclic center Forum Math. (IF 0.8) Pub Date : 2024-01-01 Diego García-Lucas, Leo Margolis
We show that the modular isomorphism problem has a positive answer for groups of nilpotency class 2 with cyclic center, i.e., that for such p-groups G and H an isomorphism between the group algebras FG and FH implies an isomorphism of the groups G and H for F the field of p elements. For groups of odd order this implication is also proven for F being any field of characteristic p. For groups of even
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L-series of weakly holomorphic quasimodular forms and a converse theorem Forum Math. (IF 0.8) Pub Date : 2024-01-01 Mrityunjoy Charan
We define L-series of weakly holomorphic quasimodular forms and we derive functional equations of those L-series. We also prove a converse theorem for weakly holomorphic quasimodular forms.
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Sharp Sobolev and Adams–Trudinger–Moser embeddings on weighted Sobolev spaces and their applications Forum Math. (IF 0.8) Pub Date : 2024-01-01 João Marcos do Ó, Guozhen Lu, Raoní Ponciano
We derive sharp Sobolev embeddings on a class of Sobolev spaces with potential weights without assuming any boundary conditions. Moreover, we consider the Adams-type inequalities for the borderline Sobolev embedding into the exponential class with a sharp constant. As applications, we prove that the associated elliptic equations with nonlinearities in both forms of polynomial and exponential growths
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Two curious q-supercongruences and their extensions Forum Math. (IF 0.8) Pub Date : 2024-01-01 Haihong He, Xiaoxia Wang
We prove two single-parameter q-supercongruences which were recently conjectured by Guo, and establish their further extensions with one more parameter. Crucial ingredients in the proof are the terminating form of the q-binomial theorem, a Karlsson–Minton-type summation formula due to Gasper, and the method of “creative microscoping” developed by Guo and Zudilin. Incidentally, an assertion of Li, Tang
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A note on the post quantum-Sheffer polynomial sequences Forum Math. (IF 0.8) Pub Date : 2024-01-01 Subuhi Khan, Mehnaz Haneef
In this article, the post quantum analogue of Sheffer polynomial sequences is introduced using concepts of post quantum calculus. The series representation, recurrence relations, determinant expression and certain other properties of this class are established. Further, the 2D-post quantum-Sheffer polynomials are introduced via generating function and their properties are established. Certain identities
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Generalized orthogonal measures on the space of unital completely positive maps Forum Math. (IF 0.8) Pub Date : 2024-01-01 Angshuman Bhattacharya, Chaitanya J. Kulkarni
A classical result by Effros connects the barycentric decomposition of a state on a C*-algebra to the disintegration theory of the GNS representation of the state with respect to an orthogonal measure on the state space of the C*-algebra. In this note, we take this approach to the space of unital completely positive maps on a C*-algebra with values in B ( H ) {B(H)} , connecting the barycentric decomposition
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Octonionic monogenic and slice monogenic Hardy and Bergman spaces Forum Math. (IF 0.8) Pub Date : 2024-01-01 Fabrizio Colombo, Rolf Sören Kraußhar, Irene Sabadini
In this paper we discuss some basic properties of octonionic Bergman and Hardy spaces. In the first part we review some fundamental concepts of the general theory of octonionic Hardy and Bergman spaces together with related reproducing kernel functions in the monogenic setting. We explain how some of the fundamental problems in well-defining a reproducing kernel can be overcome in the non-associative
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A fixed point theorem for isometries on a metric space Forum Math. (IF 0.8) Pub Date : 2024-01-01 Andrzej Wiśnicki
We show that if X is a complete metric space with uniform relative normal structure and G is a subgroup of the isometry group of X with bounded orbits, then there is a point in X fixed by every isometry in G. As a corollary, we obtain a theorem of U. Lang (2013) concerning injective metric spaces. A few applications of this theorem are given to the problems of inner derivations. In particular, we show
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One-sided Gorenstein rings Forum Math. (IF 0.8) Pub Date : 2024-01-01 Lars Winther Christensen, Sergio Estrada, Li Liang, Peder Thompson, Junpeng Wang
Distinctive characteristics of Iwanaga–Gorenstein rings are typically understood through their intrinsic symmetry. We show that several of those that pertain to the Gorenstein global dimensions carry over to the one-sided situation, even without the noetherian hypothesis. Our results yield new relations among homological invariants related to the Gorenstein property, not only Gorenstein global dimensions
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Multiplicity of solutions for a singular system with sign-changing potential Forum Math. (IF 0.8) Pub Date : 2024-01-01 Wentao Lin, Yilan Wei
This paper focuses on a singular system with a sign-changing potential in Γ, a bounded domain with a Lipschitz boundary in ℝ d {\mathbb{R}^{d}} . By imposing appropriate conditions on the weight potential, which is allowed to change sign, we establish the existence of multiple solutions using the shape optimization approach. This study represents one of the earliest endeavors to explore and analyze