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Commuting Probability for Approximate Subgroups of a Finite Group Q. J. Math. (IF 0.7) Pub Date : 2024-04-22 Eloisa Detomi, Marta Morigi, Pavel Shumyatsky
For subsets $X,Y$ of a finite group G, we write $\mathrm{Pr} (X,Y)$ for the probability that two random elements $x\in X$ and $y\in Y$ commute. This paper addresses the relation between the structure of an approximate subgroup $A\subseteq G$ and the probabilities $\mathrm{Pr} (A,G)$ and $\mathrm{Pr} (A,A)$. The following results are obtained. Theorem 1.1: Let A be a K-approximate subgroup of a finite
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On Möbius Functions from Automorphic Forms and a Generalized Sarnak’s Conjecture Q. J. Math. (IF 0.7) Pub Date : 2024-04-21 Zhining Wei, Shifan Zhao
In this paper, we consider generalized Möbius functions associated with two types of L-functions: Rankin–Selberg L-functions of symmetric powers of distinct holomorphic cusp forms and L-functions derived from Maass cusp forms. We show that these generalized Möbius functions are weakly orthogonal to bounded sequences. As a direct corollary, a generalized Sarnak’s conjecture holds for these two types
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Algebraicity of L-values for GSP4 X GL2 and G Q. J. Math. (IF 0.7) Pub Date : 2024-04-15 David Loeffler, Óscar Rivero
We prove algebraicity results for critical L-values attached to the group ${\rm GSp}_4 \times {\rm GL}_2$, and for Gan–Gross–Prasad periods which are conjecturally related to central L-values for ${\rm GSp}_4 \times {\rm GL}_2 \times {\rm GL}_2$. Our result for ${\rm GSp}_4 \times {\rm GL}_2$ overlaps substantially with recent results of Morimoto, but our methods are very different; these results will
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A simple construction of potential operators for compensated compactness Q. J. Math. (IF 0.7) Pub Date : 2024-04-11 Bogdan Raiță
We give a short proof of the fact that each homogeneous linear differential operator $\mathscr{A}$ of constant rank admits a homogeneous potential operator $\mathscr{B}$, meaning that $$\ker\mathscr{A}(\xi)=\mathrm{im\,}\mathscr{B}(\xi) \quad\text{for }\xi\in\mathbb{R}^n\backslash\{0\}.$$ We make some refinements of the original result and some related remarks.
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HKT Manifolds: Hodge Theory, Formality and Balanced Metrics Q. J. Math. (IF 0.7) Pub Date : 2024-04-05 Giovanni Gentili, Nicoletta Tardini
Let $(M,I,J,K,\Omega)$ be a compact HKT manifold, and let us denote with $\partial$ the conjugate Dolbeault operator with respect to I, $\partial_J:=J^{-1}\overline\partial J$, $\partial^\Lambda:=[\partial,\Lambda]$, where Λ is the adjoint of $L:=\Omega\wedge-$. Under suitable assumptions, we study Hodge theory for the complexes $(A^{\bullet,0},\partial,\partial_J)$ and $(A^{\bullet,0},\partial,\partial^\Lambda)$
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Higher-degree Artin conjecture Q. J. Math. (IF 0.7) Pub Date : 2024-04-05 Olli Järviniemi
For an algebraic number α we consider the orders of the reductions of α in finite fields. In the case where α is an integer, it is known by the work on Artin’s primitive root conjecture that the order is ‘almost always almost maximal’ assuming the Generalized Riemann Hypothesis (GRH), but unconditional results remain modest. We consider higher-degree variants under GRH. First, we modify an argument
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Sectorial Equidistribution of the Roots of x2 + 1 Modulo Primes Q. J. Math. (IF 0.7) Pub Date : 2024-03-28 Evgeny Musicantov, Sa’ar Zehavi
The equation $x^2 + 1 = 0\mod p$ has solutions whenever p = 2 or $4n + 1$. A famous theorem of Fermat says that these primes are exactly the ones that can be described as a sum of two squares. The roots of the former equation are equidistributed is a beautiful theorem of Duke, Friedlander and Iwaniec. The angles associated to the representation of such prime as a sum of squares are equidistributed
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The space of closed G2-structures. I. Connections Q. J. Math. (IF 0.7) Pub Date : 2024-03-20 Pengfei Xu, Kai Zheng
In this article, we develop foundational theory for geometries of the space of closed G2-structures in a given cohomology class as an infinite-dimensional manifold. We construct Levi-Civita connections for Sobolev-type metrics, formulate geodesic equations and analyze the variational structures of torsion-free G2-structures under these Sobolev-type metrics.
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An Explicit Vinogradov–Korobov Zero-Free Region for Dirichlet L-Functions Q. J. Math. (IF 0.7) Pub Date : 2024-03-18 Tanmay Khale
We establish the first explicit form of the Vinogradov–Korobov zero-free region for Dirichlet L-functions.
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Boundedness of Differential Transforms for Poisson Semigroups Generated by Bessel Operators Q. J. Math. (IF 0.7) Pub Date : 2024-03-18 Chao Zhang
In this paper we analyze the convergence of the following type of series: $$ T_N \,\,f(x)=\sum_{j=N_1}^{N_2} v_j\Big({\mathcal P}_{a_{j+1}} \,\,f(x)-{\mathcal P}_{a_{j}} \,\,f(x)\Big),\quad x\in \mathbb R_+, $$ where $\{{\mathcal P}_{t} \}_{t\gt0}$ is the Poisson semigroup associated with the Bessel operator $\displaystyle \Delta_\lambda:=-{d^2\over dx^2}-{2\lambda\over x}{d\over dx}$, with λ being
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A Rademacher-type exact formula for partitions without sequences Q. J. Math. (IF 0.7) Pub Date : 2024-02-29 Walter Bridges, Kathrin Bringmann
In this paper, we prove an exact formula for the number of partitions without sequences. By work of Andrews, the corresponding generating function is a mixed mock modular form weight of 0. The proof requires evaluating and bounding Kloosterman sums and the Circle Method.
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Universality theorems of Selberg zeta functions for arithmetic groups Q. J. Math. (IF 0.7) Pub Date : 2024-02-29 Yasufumi Hashimoto
We prove a universality theorem for the Selberg zeta function of subgroups of $\mathrm{SL}_2(\mathbb{Z})$ or co-compact arithmetic groups derived from quaternion algebras, in the strip $\{5/6 \lt \mathrm{Re}{s} \lt 1\}$, improving the range compared with a previous work by Drungilas–Garunkštis–Kačenas. We also obtain the same range for a joint universality theorem for congruence subgroups, which improves
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An ErdŐs–Kac theorem for integers with dense divisors Q. J. Math. (IF 0.7) Pub Date : 2024-02-21 Gérald Tenenbaum, Andreas Weingartner
We show that for large integers n, whose ratios of consecutive divisors are bound above by an arbitrary constant, the number of prime factors follows an approximate normal distribution, with mean $C \log_2 n$ and variance $V \log_2 n$, where $C=1/(1-{\rm e}^{-\gamma})\approx 2.280$ and V ≈ 0.414. This result is then generalized in two different directions.
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A mode of convergence arising in diffusive relaxation Q. J. Math. (IF 0.7) Pub Date : 2024-02-20 Nuno J Alves, João Paulos
In this work, a mode of convergence for measurable functions is introduced. A related notion of Cauchy sequence is given, and it is proved that this notion of convergence is complete in the sense that Cauchy sequences converge. Moreover, the preservation of convergence under composition is investigated. The origin of this mode of convergence lies in the path of proving that the density of a Euler system
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Profinite completions of free-by-free groups contain everything Q. J. Math. (IF 0.7) Pub Date : 2024-02-17 Martin R Bridson
Given an arbitrary, finitely presented, residually finite group Γ, one can construct a finitely generated, residually finite, free-by-free group $M_\Gamma = F_\infty\rtimes F_4$ and an embedding $M_\Gamma \hookrightarrow (F_4\ast \Gamma)\times F_4$ that induces an isomorphism of profinite completions. In particular, there is a free-by-free group whose profinite completion contains $\widehat{\Gamma}$
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Value Distribution of Logarithmic Derivatives of Quadratic Twists of Automorphic L-functions Q. J. Math. (IF 0.7) Pub Date : 2024-01-16 Amir Akbary, Alia Hamieh
Let $d\in\mathbb{N}$ and π be a fixed cuspidal automorphic representation of $\mathrm{GL}_{d}(\mathbb{A}_{\mathbb{Q}})$ with unitary central character. We determine the limiting distribution of the family of values $-\frac{L^{\prime}}{L}(1+it,\pi\otimes\chi_D)$ as D varies over fundamental discriminants. Here, t is a fixed real number and χD is the real character associated with D. We establish an
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Non-formality of Voronov’s Swiss-Cheese operads Q. J. Math. (IF 0.7) Pub Date : 2024-01-04 Najib Idrissi, Renato Vasconcellos Vieira
The Swiss-Cheese operads, which encode actions of algebras over the little n-cubes operad on algebras over the little $(n-1)$-cubes operad, comes in several variants. We prove that the variant in which open operations must have at least one open input is not formal in characteristic zero. This is slightly stronger than earlier results of Livernet and Willwacher. The obstruction to formality that we
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A version of Kalton’s theorem for the space of regular homogeneous polynomials on Banach lattices Q. J. Math. (IF 0.7) Pub Date : 2023-10-28 Qingying Bu
We give a version of Kalton’s theorem for the space of regular homogeneous polynomials on Banach lattices. As applications, we obtain sufficient conditions for the reflexivity of ${\mathcal P}^r(^nE;F)$, the space of regular n-homogeneous polynomials from a Banach lattice E to a Banach lattice F, and sufficient conditions for the positive Grothendieck property of $\hat{\otimes}_{n,s,|\pi|}E$, the n-fold
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The Bruce–Roberts Numbers of a Function on an ICIS Q. J. Math. (IF 0.7) Pub Date : 2023-10-24 B K Lima-Pereira, J J Nuno-Ballesteros, B Orefice-Okamoto, J N Tomazella
We relate a number of invariants of a function germ with isolated singularity over an isolated complete intersection singularity (ICIS), generalizing our previous results, [17, 18], as a consequence we present a new relatively elementary proof of Greuel’s theorem that for a weighted homogeneous ICIS the Milnor number is equal to Tjurina number. With this relation, we are able to prove that the relative
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Dirichlet is not just bad and singular in many rational IFS fractals Q. J. Math. (IF 0.7) Pub Date : 2023-10-14 Johannes Schleischitz
For $m\ge 2$, consider K the m-fold Cartesian product of the limit set of an iterated function system (IFS) of two affine maps with rational coefficients. If the contraction rates of the IFS are reciprocals of integers, and K does not degenerate to singleton, we construct vectors in K that lie within the ‘folklore set’ as defined by Beresnevich et al., meaning that they are Dirichlet improvable but
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Frobenius constants for families of elliptic curves Q. J. Math. (IF 0.7) Pub Date : 2023-08-23 Bidisha Roy, Masha Vlasenko
The paper deals with a class of periods, Frobenius constants, which describe monodromy of Frobenius solutions of differential equations arising in algebraic geometry. We represent Frobenius constants related to families of elliptic curves as iterated integrals of modular forms. Using the theory of periods of modular forms, we then witness some of these constants in terms of zeta values.
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nℤ-abelian and nℤ-exact categories Q. J. Math. (IF 0.7) Pub Date : 2023-08-21 Ramin Ebrahimi, Alireza Nasr-Isfahani
In this paper, we introduce $n\mathbb{Z}$-abelian and $n\mathbb{Z}$-exact categories by axiomatizing properties of $n\mathbb{Z}$-cluster tilting subcategories. We study these categories and show that every $n\mathbb{Z}$-cluster tilting subcategory of an abelian (resp., exact) category has a natural structure of an $n\mathbb{Z}$-abelian (resp., $n\mathbb{Z}$-exact) category. Also, we show that every
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The prime number theorem for primes in arithmetic progressions at large values Q. J. Math. (IF 0.7) Pub Date : 2023-08-10 Ethan Simpson Lee
Assuming the Riemann hypothesis, we prove the latest explicit version of the prime number theorem for short intervals. Using this result, and assuming the generalised Riemann hypothesis for Dirichlet L-functions is true, we then establish explicit formulae for $\psi(x,\chi)$, $\theta(x,\chi)$ and an explicit version of the prime number theorem for primes in arithmetic progressions that hold for general
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Morse numbers of function germs with isolated singularities Q. J. Math. (IF 0.7) Pub Date : 2023-08-10 Laurenţiu Maxim, Mihai TibĂr
A set of Morse numbers is associated with a holomorphic function germ with stratified isolated singularity, extending the classical Milnor–Morse number to the setting of a singular base space.
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Sums of singular series with large sets and the tail of the distribution of primes Q. J. Math. (IF 0.7) Pub Date : 2023-07-19 Vivian Kuperberg
In 1976, Gallagher showed that the Hardy–Littlewood conjectures on prime k-tuples imply that the distribution of primes in log-size intervals is Poissonian. He did so by computing average values of the singular series constants over different sets of a fixed size k contained in an interval $[1,h]$ as $h \to \infty$, and then using this average to compute moments of the distribution of primes. In this
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A remark on the characteristic elements of anticyclotomic Selmer groups of elliptic curves with complex multiplication at supersingular primes Q. J. Math. (IF 0.7) Pub Date : 2023-07-19 Antonio Lei
Let $p\ge5$ be a prime number. Let $E/\mathbb{Q}$ be an elliptic curve with complex multiplication by an imaginary quadratic field K such that p is inert in K and that E has good reduction at p. Let $K_\infty$ be the anticyclotomic $\mathbb{Z}_p$-extension of K. Agboola–Howard defined Kobayashi-type signed Selmer groups of E over $K_\infty$ and showed that exactly one of them is cotorsion over the
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Join operation and A-finite map-germs Q. J. Math. (IF 0.7) Pub Date : 2023-07-11 M E Rodrigues Hernandes, M A S Ruas
In this work we define some map-germs, called elementary joins, for the purpose of producing new ${\mathcal A}$-finite map-germs from them. In particular, we describe a general form of an ${\mathcal A}$-finite monomial map from $(\mathbb{C}^n,0)$ to $(\mathbb{C}^{p},0)$ for $p\geq 2n$ of any corank in terms of elementary join maps. Our main tools are the delta invariant and some invariants of curves
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Sutured manifolds and ℓ2-Betti numbers Q. J. Math. (IF 0.7) Pub Date : 2023-07-05 Gerrit Herrmann
Using the virtual fibering theorem of Agol, we show that a sutured 3-manifold $(M, R_{+},R_{-},\gamma)$ is taut if and only if the $\ell^{2}$-Betti numbers of the pair $(M,R_{-})$ are zero. As an application, we can characterize Thurston norm minimizing surfaces in a 3-manifold N with empty or toroidal boundary by the vanishing of certain $\ell^{2}$-Betti numbers.
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Anti-instantons on a class of quaternionic Kähler manifolds Q. J. Math. (IF 0.7) Pub Date : 2023-06-10 Udhav Fowdar
We construct the first examples of (abelian) anti-instantons on certain non-compact quaternionic Kähler 8-manifolds and by contrast we show that no abelian anti-instantons exist on compact quaternionic Kähler 8-manifolds.
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Three instability stratifications of the stack of Higgs bundles on a smooth projective curve Q. J. Math. (IF 0.7) Pub Date : 2023-06-10 Eloise Hamilton
We study three instability stratifications of the stack of twisted Higgs bundle of a fixed rank and degree on a smooth complex projective curve. The first is the Harder–Narasimhan (HN) stratification, defined by the instability type of the Higgs bundle. The second is the bundle Harder–Narasimhan (bHN) stratification, defined by the instability type of the underlying bundle. While an unstable HN stratum
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Subconvexity of a double Dirichlet series over the Gaussian field Q. J. Math. (IF 0.7) Pub Date : 2023-06-09 Peng Gao, Liangyi Zhao
We establish a subconvexity bound for a double Dirichlet series involving with the quadratic Hecke L-functions over the Gaussian field.
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Equidistribution of primitive lattices in ℝn Q. J. Math. (IF 0.7) Pub Date : 2023-06-09 Tal Horesh, Yakov Karasik
We count primitive lattices of rank d inside $\mathbb{Z}^{n}$ as their covolume tends to infinity, with respect to certain parameters of such lattices. These parameters include, for example, the subspace that a lattice spans, namely its projection to the Grassmannian; its homothety class and its equivalence class modulo rescaling and rotation, often referred to as a shape. We add to a prior work of
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Ω-bounds for the partial sums of some modified Dirichlet characters Q. J. Math. (IF 0.7) Pub Date : 2023-06-09 MARCO AYMONE
We consider the problem of Ω bounds for the partial sums of a modified character, i.e., a completely multiplicative function f such that $f(p)=\chi(p)$ for all but a finite number of primes p, where χ is a primitive Dirichlet character. We prove that in some special circumstances, $\sum_{n\leq x}f(n)=\Omega((\log x)^{|S|})$, where S is the set of primes p, where $f(p)\neq \chi(p)$. This gives credence
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Quantitative results of the Romanov type representation functions Q. J. Math. (IF 0.7) Pub Date : 2023-06-08 Yong-Gao Chen, Yuchen Ding
For α > 0, let$$\mathscr{A}=\{a_1 \lt a_2 \lt a_3\lt\cdots\}$$and$$\mathscr{L}=\{\ell_1, \ell_2, \ell_3,\cdots\} \quad \text{(not\ necessarily\ different)}$$be two sequences of positive integers with $\mathscr{A}(m)\gt(\log m)^\alpha $ for infinitely many positive integers m and $\ell_m\lt0.9\log\log m$ for sufficiently large integers m. Suppose further that $(\ell_i,a_i)=1$ for all i. For any n, let
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Small fractional parts of binary forms Q. J. Math. (IF 0.7) Pub Date : 2023-06-08 Kiseok Yeon
We obtain bounds on fractional parts of binary forms of the shape with $\alpha_k,\alpha_l,\ldots,\alpha_0\in{\mathbb R}$ and $l\leq k-2.$ By exploiting recent progress on Vinogradov’s mean value theorem and earlier work on exponential sums over smooth numbers, we derive estimates superior to those obtained hitherto for the best exponent σ, depending on k and $l,$ such that
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Mahler measure of a non-reciprocal family of elliptic curves Q. J. Math. (IF 0.7) Pub Date : 2023-05-11 Detchat Samart
In this article, we study the logarithmic Mahler measure of the one-parameter family $$Q_\alpha=y^2+(x^2-\alpha x)y+x,$$ denoted by $\mathrm{m}(Q_\alpha)$. The zero loci of Qα generically define elliptic curves Eα, which are 3-isogenous to the family of Hessian elliptic curves. We are particularly interested in the case $\alpha\in (-1,3)$, which has not been considered in the literature due to certain
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On the Balog–Ruzsa theorem in short intervals Q. J. Math. (IF 0.7) Pub Date : 2023-04-17 Yu-Chen Sun
In this paper we give a short interval version of the Balog–Ruzsa theorem concerning bounds for the L1 norm of the exponential sum over r-free numbers. In particular, when r = 2, for $H \geq N^{\frac{9}{17}+\epsilon}$, we have the lower bound result and for $H \geq N^{\frac{18}{29}+\epsilon}$, we have the upper bound result As an application, we show that the L1 norm of the exponential sum $\sum_{|n-N|
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Riemann–roch theorems in monoidal 2-categories Q. J. Math. (IF 0.7) Pub Date : 2023-04-08 Jonathan A Campbell, Kate Ponto
Smooth and proper dg-algebras have an Euler class valued in the Hochschild homology of the algebra. This Euler class is worthy of this name since it satisfies many familiar properties including compatibility with the pairing on the Hochschild homology of the algebra and that of its opposite. This compatibility is the Riemann–Roch theorems of [21, 14]. In this paper, we prove a broad generalization
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Quantum modular forms from real-quadratic double sums Q. J. Math. (IF 0.7) Pub Date : 2023-03-31 Kathrin Bringmann, Caner Nazaroglu
In 2015, Lovejoy and Osburn discovered 12 q-hypergeometric series and proved that their Fourier coefficients can be understood as counting functions of ideals in certain quadratic fields. In this paper, we study their modular and quantum modular properties and show that they yield three vector-valued quantum modular forms on the group $\Gamma_0 (2)$.
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Instantons on Sasakian 7-manifolds Q. J. Math. (IF 0.7) Pub Date : 2023-03-31 Luis E Portilla, Henrique N SÁ Earp
We study a natural contact instanton equation on gauge fields over 7-dimensional Sasakian manifolds, which is closely related to both the transverse Hermitian Yang–Mills (HYM) condition and the G2-instanton equation. We obtain, by Fredholm theory, a finite-dimensional local model for the moduli space of irreducible solutions. Following the approach by Baraglia and Hekmati in five dimensions [1], we
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Combinatorial classification of (±1)-skew projective spaces Q. J. Math. (IF 0.7) Pub Date : 2023-03-07 Akihiro Higashitani, Kenta Ueyama
The non-commutative projective scheme $\operatorname{\mathsf{Proj_{nc}}} S$ of a $(\pm 1)$-skew polynomial algebra S in n variables is considered to be a $(\pm 1)$-skew projective space of dimension n − 1. In this paper, using combinatorial methods, we give a classification theorem for $(\pm 1)$-skew projective spaces. Specifically, among other equivalences, we prove that $(\pm 1)$-skew projective
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Inverse square singularities and eigenparameter-dependent boundary conditions are two sides of the same coin Q. J. Math. (IF 0.7) Pub Date : 2023-02-20 Namig J Guliyev
We show that inverse square singularities can be treated as boundary conditions containing rational Herglotz–Nevanlinna functions of the eigenvalue parameter with ‘a negative number of poles’. More precisely, we treat in a unified manner one-dimensional Schrödinger operators with either an inverse square singularity or a boundary condition containing a rational Herglotz–Nevanlinna function of the eigenvalue
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Singular quiver varieties over extended dynkin quivers Q. J. Math. (IF 0.7) Pub Date : 2023-02-20 Gard Olav Helle
We classify the singularities in the unframed Nakajima quiver varieties associated with extended Dynkin quivers and the corresponding minimal imaginary root with a small restriction on the parameters and use this to construct a number of hyper-Kähler cobordisms between binary polyhedral spaces.
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A comparison of dg algebra resolutions with prime residual characteristic Q. J. Math. (IF 0.7) Pub Date : 2023-02-17 Michael DeBellevue, Josh Pollitz
In this article, we fix a prime integer p and compare certain dg algebra resolutions over a local ring whose residue field has characteristic p. Namely, we show that given a closed surjective map between such algebras there is a precise description for the minimal model in terms of the acyclic closure and that the latter is a quotient of the former. A first application is that the homotopy Lie algebra
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Filtrations on the representation ring of an affine algebraic group Q. J. Math. (IF 0.7) Pub Date : 2023-01-10 Nikita A Karpenko
Let G be an affine algebraic group over a field. The representation ring $\mathrm{R}(G)$ has three standard filtrations, defining the same topology on $\mathrm{R}(G)$: augmentation, Chern and Chow, each of which contained in the next one. For split reductive G, motivated by potential applications related to spin groups, we introduce and study one more filtration, containing the previous ones, which
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Stratification and the comparison between homological and tensor triangular support Q. J. Math. (IF 0.7) Pub Date : 2022-12-27 Tobias Barthel, Drew Heard, Beren Sanders
We compare the homological support and tensor triangular support for ‘big’ objects in a rigidly-compactly generated tensor triangulated category. We prove that the comparison map from the homological spectrum to the tensor triangular spectrum is a bijection and that the two notions of support coincide whenever the category is stratified, extending the work of Balmer. Moreover, we clarify the relations
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Hitchin WKB-problem and P = W conjecture in lowest degree for rank 2 over the 5-punctured sphere Q. J. Math. (IF 0.7) Pub Date : 2022-12-21 Szilárd Szabó
We use abelianization of Higgs bundles away from the ramification divisor and fiducial solutions to analyze the large-scale behavior of Fenchel–Nielsen co-ordinates on the moduli space of rank 2 Higgs bundles on the Riemann sphere with five punctures. We solve the related Hitchin WKB problem and prove the lowest degree weighted pieces of the P = W conjecture in this case.
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Counting integral points on indefinite ternary quadratic equations over number fields Q. J. Math. (IF 0.7) Pub Date : 2022-12-07 Fei Xu, Runlin Zhang
We study an asymptotic formula for counting integral points over an equation defined by a non-degenerate indefinite integral ternary quadratic form f representing a non-zero integer a such that $-a\cdot det(\,f)$ is square over a number field. In particular, we prove that the leading coefficient of this asymptotic formula is given by the product of local densities normalized by $1-p^{-1}$ over all
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Basic kirwan injectivity and its applications Q. J. Math. (IF 0.7) Pub Date : 2022-12-03 Yi Lin, Xiangdong Yang
Consider the Hamiltonian action of a torus on a transversely symplectic foliation that is also Riemannian. When the transverse hard Lefschetz property is satisfied, we establish a foliated version of the Kirwan injectivity theorem and use it to study Hamiltonian torus actions on transversely Kähler foliations. Among other things, we prove a foliated analogue of the Carrell–Liberman theorem. As an application
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Paley graphs and sárközy’s theorem in function fields Q. J. Math. (IF 0.7) Pub Date : 2022-12-01 Eric Naslund
Sárközy’s theorem states that dense sets of integers must contain two elements whose difference is a kth power. Following the polynomial method breakthrough of Croot, Lev and Pach [3], Green proved a strong quantitative version of this result for $\mathbb{F}_{q}[T]$. In this paper we provide a lower bound for Sárközy’s theorem in function fields by adapting Ruzsa’s construction [17] for the analogous
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On weak compactness in projective tensor products Q. J. Math. (IF 0.7) Pub Date : 2022-11-29 José Rodríguez
We study the property of being strongly weakly compactly generated (and some relatives) in projective tensor products of Banach spaces. Our main result is as follows. Let $1 \unicode{x003C} p,q\unicode{x003C}\infty$ be such that $1/p+1/q\geq 1$. Let X (resp., Y) be a Banach space with a countable unconditional finite-dimensional Schauder decomposition having a disjoint lower p-estimate (resp., q-estimate)
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Quantifying conjugacy separability in wreath products of groups Q. J. Math. (IF 0.7) Pub Date : 2022-11-25 Michal Ferov, Mark Pengitore
We study generalizations of conjugacy separability in restricted wreath products of groups. We provide an effective upper bound for $\mathcal{C}$-conjugacy separability of a wreath product $A \wr B$ in terms of the $\mathcal{C}$-conjugacy separability of A and B, the growth of $\mathcal{C}$-cyclic subgroup separability of B and the $\mathcal{C}$-residual girth of $B.$ As an application, we provide
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Twists of rational Cherednik algebras Q. J. Math. (IF 0.7) Pub Date : 2022-11-14 Y Bazlov, E Jones-Healey, A Mcgaw, A Berenstein
We show that braided Cherednik algebras introduced by Bazlov and Berenstein are cocycle twists of rational Cherednik algebras of the imprimitive complex reflection groups $G(m,p,n)$, when m is even. This gives a new construction of mystic reflection groups which have Artin–Schelter regular rings of quantum polynomial invariants. As an application of this result, we show that a braided Cherednik algebra
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Homotopy epimorphisms and derived tate’s acyclicity for commutative C*-algebras Q. J. Math. (IF 0.7) Pub Date : 2022-09-29 Federico Bambozzi, Tomoki Mihara
We study homotopy epimorphisms and covers formulated in terms of derived Tate’s acyclicity for commutative $C^*$-algebras and algebras of continuous functions valued in non-Archimedean valued fields. We prove that a homotopy epimorphism between commutative $C^*$-algebras precisely corresponds to a closed immersion between the compact Hausdorff topological spaces associated with them and a cover of
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Subconvexity in Inhomogeneous Vinogradov Systems Q. J. Math. (IF 0.7) Pub Date : 2022-08-29 Trevor D Wooley
When k and s are natural numbers and ${\mathbf h}\in {\mathbb Z}^k$, denote by $J_{s,k}(X;\,{\mathbf h})$ the number of integral solutions of the system $$ \sum_{i=1}^s(x_i^j-y_i^j)=h_j\quad (1\leqslant j\leqslant k), $$ with $1\leqslant x_i,y_i\leqslant X$. When $s\lt k(k+1)/2$ and $(h_1,\ldots ,h_{k-1})\ne {\mathbf 0}$, Brandes and Hughes have shown that $J_{s,k}(X;\,{\mathbf h})=o(X^s)$. In this
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Wide moments of L-functions II: dirichlet L-functions Q. J. Math. (IF 0.7) Pub Date : 2022-08-26 Asbjørn christian Nordentoft
We study wide moments of Dirichlet L-functions using analytic properties of the Lerch zeta function. Among other things we obtain an asymptotic expansion of wide moments of Dirichlet L-functions (with arbitrary twists) extending results of Heath-Brown. We also give applications to non-vanishing.
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Totally disconnected semigroup compactifications of topological groups Q. J. Math. (IF 0.7) Pub Date : 2022-08-19 Alexander Stephens, Ross Stokke
We introduce the notion of an introverted Boolean algebra $\mathcal{B}$ of closed-and-open subsets of a topological group G show that the associated Stone space $(\nu_{\mathcal{B}} G, \nu_{\mathcal{B}})$ is a totally disconnected semigroup compactification of G and show that every totally disconnected semigroup compactification of G takes this form. We identify and study the universal totally disconnected
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Variants Of the Selberg Sieve and Almost Prime K-tuples Q. J. Math. (IF 0.7) Pub Date : 2022-08-13 Paweł Lewulis
Let $k\geqslant 2$ and $\mathcal{P} (n) = (A_1 n + B_1 ) \cdots (A_k n + B_k)$ where all the $A_i, B_i$ are integers. Suppose that $\mathcal{P} (n)$ has no fixed prime divisors. For each choice of k it is known that there exists an integer ϱk such that $\mathcal{P} (n)$ has at most ϱk prime factors infinitely often. We used a new weighted sieve setup combined with a device called ɛ-trick to improve
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Sobolev regularity for linear growth functionals acting on ℂ-elliptic operators Q. J. Math. (IF 0.7) Pub Date : 2022-08-11 Piotr Wozniak
In this paper, we prove the higher Sobolev regularity of minimizers for convex integral functionals evaluated on linear differential operators of order one. This work intends to generalize the already existing theory for the cases of full and symmetric gradients to the entire class of ${\mathbb C}$-elliptic operators therein including the trace-free symmetric gradient for dimension $n \geq 3$.
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Bounds for del pezzo surfaces of degree two Q. J. Math. (IF 0.7) Pub Date : 2022-08-04 Aritra Ghosh, Sumit Kumar, Kummari Mallesham, Saurabh Kumar Singh
In this article, we obtain an upper bound for the number of integral points on del Pezzo surfaces of degree two.