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Submersions, immersions, and étale maps in diffeology Indag. Math. (IF 0.6) Pub Date : 2024-03-20 Alireza Ahmadi
Although structural maps such as subductions and inductions appear naturally in diffeology, one of the challenges is providing suitable analogues for submersions, immersions, and étale maps (i.e., local diffeomorphisms) consistent with the classical versions of these maps between manifolds. In this paper, we consider diffeological or plotwise versions of submersions, immersions, and étale maps as an
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A characterisation of linear repetitivity for cut and project sets with general polytopal windows Indag. Math. (IF 0.6) Pub Date : 2024-03-19 James J. Walton
The cut and project method is a central construction in the theory of Aperiodic Order for generating quasicrystals with pure point diffraction. Linear repetitivity () is a form of ideal regularity of aperiodic patterns. Recently, Koivusalo and the present author characterised for cut and project sets with convex polytopal windows whose supporting hyperplanes are commensurate with the lattice, the weak
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Quantum superintegrable spin systems on graph connections Indag. Math. (IF 0.6) Pub Date : 2024-03-16 Nicolai Reshetikhin, Jasper Stokman
In this paper we construct certain quantum spin systems on moduli spaces of -connections on a connected oriented finite graph, with a simply connected compact Lie group. We construct joint eigenfunctions of the commuting quantum Hamiltonians in terms of local invariant tensors. We determine sufficient conditions ensuring superintegrability of the quantum spin system using irreducibility criteria for
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Symplectic complexity of reductive group actions Indag. Math. (IF 0.6) Pub Date : 2024-03-16 Avraham Aizenbud, Dmitry Gourevitch
Let a complex algebraic reductive group act on a complex algebraic manifold . For a -invariant subvariety of the nilpotent cone we define a notion of -symplectic complexity of . This notion generalizes the notion of complexity defined in Vinberg (1986). We prove several properties of this notion, and relate it to the notion of -complexity defined in Aizenbud and Gourevitch (2024) motivated by its relation
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Generating operators of symmetry breaking — From discrete to continuous Indag. Math. (IF 0.6) Pub Date : 2024-03-15 Toshiyuki Kobayashi
Based on the “generating operator” of the Rankin–Cohen bracket introduced in Kobayashi–Pevzner [arXiv:2306.16800], we present a method to construct various fundamental operators with continuous parameters such as invariant trilinear forms on infinite-dimensional representations, the Fourier and the Poisson transforms on the anti-de Sitter space, and integral symmetry breaking operators for the fusion
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Berezin quantization and representation theory Indag. Math. (IF 0.6) Pub Date : 2024-03-15 V.F. Molchanov
We present an approach to Berezin quantization (a variant of quantization in the spirit of Berezin) on para-Hermitian symmetric spaces using the notion of an “overgroup”. This approach gives covariant and contravariant symbols and the Berezin transform in a natural and transparent way.
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Symmetric pairs and branching laws Indag. Math. (IF 0.6) Pub Date : 2024-03-15 Paul-Émile Paradan
Let be a compact connected Lie group and let be a subgroup fixed by an involution. A classical result assures that the -action on the flag variety of admits a finite number of orbits. In this article we propose a formula for the branching coefficients of the symmetric pair that is parametrized by .
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Large deviation principle of multiplicative Ising models on Markov–Cayley trees Indag. Math. (IF 0.6) Pub Date : 2024-03-13 Jung-Chao Ban, Wen-Guei Hu, Zongfan Zhang
In this paper, we study the large deviation principle (LDP) for two types (Type I and Type II) of multiplicative Ising models. For Types I and II, the explicit formulas for the free energy functions and the associated rate functions are derived. Furthermore, we prove that those free energy functions are differentiable, which indicates that both systems are characterized by a lack of phase transition
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Riesz completions of some spaces of regular operators Indag. Math. (IF 0.6) Pub Date : 2024-03-13 A.W. Wickstead
We describe the Riesz completion (in the sense of van Haandel) of some spaces of regular operators as explicitly identified subspaces of the regular operators into larger range spaces.
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Solvability of Vekua-type periodic operators and applications to classical equations Indag. Math. (IF 0.6) Pub Date : 2024-03-06 Alexandre Kirilov, Wagner Augusto Almeida de Moraes, Pedro Meyer Tokoro
In this note, we investigate Vekua-type periodic operators of the form , where is a constant coefficient partial differential operator. We provide a complete characterization of the necessary and sufficient conditions for the solvability and global hypoellipticity of . As an application, we provide a comprehensive characterization of Vekua-type operators associated with classical wave, heat, and Laplace
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Explicit dynamical systems on the Sierpiński carpet Indag. Math. (IF 0.6) Pub Date : 2024-02-23 Worapan Homsomboon
We apply Boroński and Oprocha’s inverse limit construction of dynamical systems on the Sierpiński carpet by using the initial systems of Chamanara surfaces and their baker transformations, . We show that all positive real numbers are realized as metric entropy values of dynamical systems on the carpet. We also produce a simplification of Boroński and Oprocha’s proof showing that dynamical systems on
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On the friable mean-value of the Erdős–Hooley Delta function Indag. Math. (IF 0.6) Pub Date : 2024-02-16 B. Martin, G. Tenenbaum, J. Wetzer
For integer and real , define . Then, put We provide uniform upper and lower bounds for the mean-value of over friable integers, i.e. integers free of large prime factors.
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Qℓ-cohomology projective planes from Enriques surfaces in odd characteristic Indag. Math. (IF 0.6) Pub Date : 2024-02-05 Matthias Schütt
We give a complete classification of -cohomology projective planes with isolated ADE-singularities and numerically trivial canonical bundle in odd characteristic. This leads to a beautiful relation with certain Enriques surfaces which parallels the situation in characteristic zero, yet displays intriguing subtleties.
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Critical curves of rotations Indag. Math. (IF 0.6) Pub Date : 2024-02-04 John A.G. Roberts, Asaki Saito, Franco Vivaldi
In rotations with a binary symbolic dynamics, a critical curve is the locus of parameters for which the boundaries of the partition that defines the symbolic dynamics are connected via a prescribed number of iterations and symbolic itinerary. We study the arithmetical and geometrical properties of these curves in parameter space.
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Tensor product of representations of quivers Indag. Math. (IF 0.6) Pub Date : 2024-01-28 Pradeep Das, Umesh V. Dubey, N. Raghavendra
In this article, we define the tensor product V⊗W of a representation V of a quiver Q with a representation W of an another quiver Q′, and show that the representation V⊗W is semistable if V and W are semistable. We give a relation between the universal representations on the fine moduli spaces N1,N2 and N3 of representations of Q,Q′ and Q⊗Q′ respectively over arbitrary algebraically closed fields
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Ranks of elliptic curves in cyclic sextic extensions of Q Indag. Math. (IF 0.6) Pub Date : 2024-01-24 Hershy Kisilevsky, Masato Kuwata
For an elliptic curve E/Q we show that there are infinitely many cyclic sextic extensions K/Q such that the Mordell-Weil group E(K) has rank greater than the subgroup of E(K) generated by all the E(F) for the proper subfields F⊂K. For certain curves E/Q we show that the number of such fields K of conductor less than X is ≫X.
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A threshold for the best two-term underapproximation by Egyptian fractions Indag. Math. (IF 0.6) Pub Date : 2024-01-24 Hùng Việt Chu
Let G be the greedy algorithm that, for each θ∈(0,1], produces an infinite sequence of positive integers (an)n=1∞ satisfying ∑n=1∞1/an=θ. For natural numbers p
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Computing the Weil representation of a superelliptic curve Indag. Math. (IF 0.6) Pub Date : 2024-01-17 Irene I. Bouw, Duc Khoi Do, Stefan Wewers
We study the Weil representation ρ of a curve over a p-adic field with potential reduction of compact type. We show that ρ can be reconstructed from its stable reduction. For superelliptic curves of the form yn=f(x) at primes p whose residue characteristic is prime to the exponent n we make this explicit.
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On some coefficients of the Artin–Hasse series modulo a prime Indag. Math. (IF 0.6) Pub Date : 2024-01-20 Marina Avitabile, Sandro Mattarei
Let be an odd prime, and let be the reduction modulo of the Artin–Hasse exponential series. We obtain a polynomial expression for in terms of those with , for even . A conjectural analogue covering the case of odd can be stated in various polynomial forms, essentially in terms of the polynomial , where denotes the th Bernoulli number.
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Normal forms for principal Poisson Hamiltonian spaces Indag. Math. (IF 0.6) Pub Date : 2024-01-09 Pedro Frejlich, Ioan Mărcuţ
We prove a normal form theorem for principal Hamiltonian actions on Poisson manifolds around the zero locus of the moment map. The local model is the generalization to Poisson geometry of the classical minimal coupling construction from symplectic geometry of Sternberg and Weinstein. Further, we show that the result implies that the quotient Poisson manifold is linearizable, and we show how to extend
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A note on the Diophantine equations 2ln2=1+q+⋯+qα and application to odd perfect numbers Indag. Math. (IF 0.6) Pub Date : 2024-01-05 Yoshinosuke Hirakawa
Let N be an odd perfect number. Then, Euler proved that there exist some integers n,α and a prime q such that N=n2qα, q∤n, and q≡α≡1mod4. In this note, we prove that the ratio σ(n2)qα is neither a square nor a square times a single prime unless α=1. It is a direct consequence of a certain property of the Diophantine equation 2ln2=1+q+⋯+qα, where l denotes one or a prime, and its proof is based on the
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On the separation of the roots of the generalized Fibonacci polynomial Indag. Math. (IF 0.6) Pub Date : 2023-12-15 Jonathan García, Carlos A. Gómez, Florian Luca
In this paper we prove some separation results for the roots of the generalized Fibonacci polynomials and their absolute values.
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p-Linear schemes for sequences modulo pr Indag. Math. (IF 0.6) Pub Date : 2023-12-14 Frits Beukers
Many interesting combinatorial sequences, such as Apéry numbers and Franel numbers, enjoy the so-called Lucas property modulo almost all primes p. Modulo prime powers pr such sequences have a more complicated behaviour which can be described by matrix versions of the Lucas property called p-linear schemes. They are generalizations of finite p-automata. In this paper we construct such p-linear schemes
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Regular models of hyperelliptic curves Indag. Math. (IF 0.6) Pub Date : 2023-12-07 Simone Muselli
Let K be a complete discretely valued field of residue characteristic not 2 and OK its ring of integers. We explicitly construct a regular model over OK with strict normal crossings of any hyperelliptic curve C/K:y2=f(x). For this purpose, we introduce the new notion of MacLane cluster picture, that aims to be a link between clusters and MacLane valuations.
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Banach function spaces done right Indag. Math. (IF 0.6) Pub Date : 2023-11-22 Emiel Lorist, Zoe Nieraeth
In this survey, we discuss the definition of a (quasi-)Banach function space. We advertise the original definition by Zaanen and Luxemburg, which does not have various issues introduced by other, subsequent definitions. Moreover, we prove versions of well-known basic properties of Banach function spaces in the setting of quasi-Banach function spaces.
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A note on the group extension problem to semi-universal deformation Indag. Math. (IF 0.6) Pub Date : 2023-11-17 An-Khuong Doan
The aim of this note is twofold. Firstly, we explain in detail Remark 4.1 in Doan (2020) by showing that the action of the automorphism group of the second Hirzebruch surface F2 on itself extends to its formal semi-universal deformation only up to the first order. Secondly, we show that for reductive group actions, the locality of the extended actions on the Kuranishi space constructed in Doan (2021)
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On the transcendence of power towers of Liouville numbers Indag. Math. (IF 0.6) Pub Date : 2023-11-11 Diego Marques, Marcelo Oliveira, Pavel Trojovský
In this paper, among other things, we explicit a Gδ-dense set of Liouville numbers, for which the triple power tower of any of its elements is a transcendental number.
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Dirac cohomology for the BGG category O Indag. Math. (IF 0.6) Pub Date : 2023-11-10 Spyridon Afentoulidis-Almpanis
We study Dirac cohomology HDg,h(M) for modules belonging to category O of a finite dimensional complex semisimple Lie algebra. We start by studying the generalized infinitesimal character decomposition of M⊗S, with S being a spin module of h⊥. As a consequence, “Vogan’s conjecture” holds, and we prove a nonvanishing result for HDg,h(M) while we show that in the case of a Hermitian symmetric pair (g
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Non-stationary α-fractal functions and their dimensions in various function spaces Indag. Math. (IF 0.6) Pub Date : 2023-11-04 Anarul Islam Mondal, Sangita Jha
In this article, we study the novel concept of non-stationary iterated function systems (IFSs) introduced by Massopust in 2019. At first, using a sequence of different contractive operators, we construct non-stationary α-fractal functions on the space of all continuous functions. Next, we provide some elementary properties of the fractal operator associated with the non-stationary α-fractal functions
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The (reflected) Eberlein convolution of measures Indag. Math. (IF 0.6) Pub Date : 2023-10-29 Daniel Lenz, Timo Spindeler, Nicolae Strungaru
In this paper, we study the properties of the Eberlein convolution of measures and introduce a reflected version of it. For functions we show that the reflected Eberlein convolution can be seen as a translation invariant function-valued inner product. We study its regularity properties and show its existence on suitable sets of functions. For translation bounded measures we show that the (reflected)
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Tangent spaces on the trianguline variety at companion points Indag. Math. (IF 0.6) Pub Date : 2023-10-28 Seginus Mowlavi
Many results about the geometry of the trianguline variety have been obtained by Breuil–Hellmann–Schraen. Among them, using geometric methods, they have computed a formula for the dimension of the tangent space of the trianguline variety at dominant crystalline generic points, which has a conjectural generalisation to companion (i.e. non-dominant) points. In an earlier work, they proved a weaker form
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Bounded compact and dual compact approximation properties of Hardy spaces: New results and open problems Indag. Math. (IF 0.6) Pub Date : 2023-10-21 Oleksiy Karlovych, Eugene Shargorodsky
The aim of the paper is to highlight some open problems concerning approximation properties of Hardy spaces. We also present some results on the bounded compact and the dual compact approximation properties (shortly, BCAP and DCAP) of such spaces, to provide background for the open problems. Namely, we consider abstract Hardy spaces H[X(w)] built upon translation-invariant Banach function spaces X
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The Mathieu conjecture for SU(2) reduced to an abelian conjecture Indag. Math. (IF 0.6) Pub Date : 2023-10-19 Michael Müger, Lars Tuset
We reduce the Mathieu conjecture for SU(2) to a conjecture about moments of Laurent polynomials in two variables with single variable polynomial coefficients.
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Pointwise attractors which are not strict Indag. Math. (IF 0.6) Pub Date : 2023-10-18 Magdalena Nowak
We deal with the finite family F of continuous maps on the Hausdorff space X. A nonempty compact subset A of such space is called a strict attractor if it has an open neighborhood U such that A=limn→∞Fn(S) for every nonempty compact S⊂U. Every strict attractor is a pointwise attractor, which means that the set {x∈X;limn→∞Fn(x)=A} contains A in its interior. We present a class of examples of pointwise
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A crossinggram for random fields on lattices Indag. Math. (IF 0.6) Pub Date : 2023-10-17 Helena Ferreira, Marta Ferreira, Luís A. Alexandre
The modeling of risk situations that occur in a space framework can be done using max-stable random fields on lattices. Although the summary coefficients for the spatial behavior do not characterize the finite-dimensional distributions of the random field, they have the advantage of being immediate to interpret and easier to estimate. The coefficients that we propose give us information about the tendency
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Counterexamples to the Hasse Principle among the twists of the Klein quartic Indag. Math. (IF 0.6) Pub Date : 2023-09-20 Elisa Lorenzo García, Michaël Vullers
In this paper we inspect from closer the local and global points of the twists of the Klein quartic. For the local ones we use geometric arguments, while for the global ones we strongly use the modular interpretation of the twists. The main result is providing families with (conjecturally infinitely many) twists of the Klein quartic that are counterexamples to the Hasse Principle.
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On nth order Euler polynomials of degree n that are Eisenstein Indag. Math. (IF 0.6) Pub Date : 2023-09-18 Michael Filaseta, Thomas Luckner
For m an even positive integer and p an odd prime, we show that the generalized Euler polynomial Emp(mp)(x) is in Eisenstein form with respect to p if and only if p does not divide m(2m−1)Bm. As a consequence, we deduce that at least 1/3 of the generalized Euler polynomials En(n)(x) are in Eisenstein form with respect to a prime p dividing n and, hence, irreducible over Q.
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On the cohomology of solvable Leibniz algebras Indag. Math. (IF 0.6) Pub Date : 2023-09-09 Jörg Feldvoss, Friedrich Wagemann
This paper is a sequel to a previous paper of the authors in which the cohomology of semi-simple Leibniz algebras was computed by using spectral sequences. In the present paper we generalize the vanishing theorems of Dixmier and Barnes for nilpotent and (super)solvable Lie algebras to Leibniz algebras. Moreover, we compute the cohomology of the one-dimensional Lie algebra with values in an arbitrary
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Amalgamation of real zero polynomials Indag. Math. (IF 0.6) Pub Date : 2023-09-06 David Sawall, Markus Schweighofer
With this article, we hope to launch the investigation of what we call the Real Zero Amalgamation Problem. Whenever a polynomial arises from another polynomial by substituting zero for some of its variables, we call the second polynomial an extension of the first one. The Real Zero Amalgamation Problem asks when two (multivariate real) polynomials have a common extension (called amalgam) that is a
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Automorphism groups of random substitution subshifts Indag. Math. (IF 0.6) Pub Date : 2023-09-01 Robbert Fokkink, Dan Rust, Ville Salo
We prove that for a suitably nice class of random substitutions, their corresponding subshifts have automorphism groups that contain an infinite simple subgroup and a copy of the automorphism group of a full shift. Hence, they are countable, non-amenable and non-residually finite. To show this, we introduce the concept of shuffles and generalised shuffles for random substitutions, as well as a local
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Geometric progressions in the sets of values of rational functions Indag. Math. (IF 0.6) Pub Date : 2023-08-26 Maciej Ulas
Let a,Q∈Q be given and consider the set G(a,Q)={aQi:i∈N} of terms of geometric progression with 0th term equal to a and the quotient Q. Let f∈Q(x,y) and Vf be the set of finite values of f. We consider the problem of existence of a,Q∈Q such that G(a,Q)⊂Vf. In the first part of the paper we describe certain classes of rational functions for which our problem has a positive solution. In the second, experimental
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On the Galois-invariant part of the Weyl group of the Picard lattice of a K3 surface Indag. Math. (IF 0.6) Pub Date : 2023-08-24 Wim Nijgh, Ronald van Luijk
Let X denote a K3 surface over an arbitrary field k. Let ks denote a separable closure of k and let Xs denote the base change of X to ks. Let O(PicX) and O(PicXs) denote the group of isometries of the lattices PicX and PicXs, respectively. Let RX denote the Galois invariant part of the Weyl group of PicXs. One can show that each element in RX can be restricted to an element of O(PicX). The following
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Weak precompactness in projective tensor products Indag. Math. (IF 0.6) Pub Date : 2023-08-24 José Rodríguez, Abraham Rueda Zoca
We give a sufficient condition for a pair of Banach spaces (X,Y) to have the following property: whenever W1⊆X and W2⊆Y are sets such that {x⊗y:x∈W1,y∈W2} is weakly precompact in the projective tensor product X⊗̂πY, then either W1 or W2 is relatively norm compact. For instance, such a property holds for the pair (ℓp,ℓq) if 1
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Remarks on weak convergence of complex Monge–Ampère measures Indag. Math. (IF 0.6) Pub Date : 2023-08-11 Mohamed El Kadiri
Let (uj) be a decreasing sequence of psh functions in the domain of definition D of the Monge–Ampère operator on a domain Ω of ℂn such that u=infjuj is plurisubharmonic on Ω. In this paper we are interested in the problem of finding conditions insuring that limj→+∞∫φ(ddcuj)n=∫φNP(ddcu)nfor any continuous function on Ω with compact support, where NP(ddcu)n is the nonpolar part of (ddcu)n, and conditions
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Conditional estimates for the logarithmic derivative of Dirichlet L-functions Indag. Math. (IF 0.6) Pub Date : 2023-07-31 Andrés Chirre, Markus Valås Hagen, Aleksander Simonič
Assuming the Generalized Riemann Hypothesis, we establish explicit bounds in the q-aspect for the logarithmic derivative L′/Lσ,χ of Dirichlet L-functions, where χ is a primitive character modulo q≥1030 and 1/2+1/loglogq≤σ≤1−1/loglogq. In addition, for σ=1 we improve upon the result by Ihara, Murty and Shimura (2009). Similar results for the logarithmic derivative of the Riemann zeta-function are given
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Algebraic independence of the partial derivatives of certain functions with arbitrary number of variables Indag. Math. (IF 0.6) Pub Date : 2023-07-28 Haruki Ide, Taka-aki Tanaka
We construct a complex entire function with arbitrary number of variables which has the following property: The infinite set consisting of all the values of all its partial derivatives of any orders at all algebraic points, including zero components, is algebraically independent. In Section 2 of this paper, we develop a technique involving linear isomorphisms and infinite products to replace the algebraic
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On integral cohomology algebra of some oriented Grassmann manifolds Indag. Math. (IF 0.6) Pub Date : 2023-07-23 Milica Jovanović
The integral cohomology algebra of G˜6,3 has been determined in the recent work of Kalafat and Yalçınkaya. We completely determine the integral cohomology algebra of G˜n,3 for n=8 and n=10. The main method used to describe these algebras is the Leray–Serre spectral sequence. We also illustrate this method by determining the integral cohomology algebra of G˜n,2 for n odd.
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Three essays on Machin’s type formulas Indag. Math. (IF 0.6) Pub Date : 2023-07-22 Armengol Gasull, Florian Luca, Juan L. Varona
We study three questions related to Machin’s type formulas. The first one gives all two terms Machin formulas where both arctangent functions are evaluated 2-integers, that is values of the form b/2a for some integers a and b. These formulas are computationally useful because multiplication or division by a power of two is a very fast operation for most computers. The second one presents a method for
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Endomorphisms and derivations of the measure algebra of commutative hypergroups Indag. Math. (IF 0.6) Pub Date : 2023-07-13 Żywilla Fechner, Eszter Gselmann, László Székelyhidi
Endomorphisms of the measure algebra of commutative hypergroups are investigated. We focus on derivations and higher order derivations which are closely related to moment function sequences of higher rank. We describe the exact connection between those higher order derivations which are endomorphisms of the measure algebra if it is considered as a module over the ring of continuous functions.
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Editorial Indag. Math. (IF 0.6) Pub Date : 2023-07-11 Onno Boxma, Michel Mandjes
Abstract not available
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Optimal cash management using impulse control Indag. Math. (IF 0.6) Pub Date : 2023-07-11 Peter Lakner, Josh Reed
We consider the impulse control of Lévy processes under the infinite horizon, discounted cost criterion. Our motivating example is the cash management problem in which a controller is charged a fixed plus proportional cost for adding to or withdrawing from his/her reserve, plus an opportunity cost for keeping any cash on hand. Our main result is to provide a verification theorem for the optimality
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Inter-model sets in Rd are model sets Indag. Math. (IF 0.6) Pub Date : 2023-07-07 Christoph Richard, Nicolae Strungaru
We show that any union of finitely many shifted model sets from a given cut-and-project scheme is a model set in some modified cut-and-project scheme. Restricting to direct space Rd, we show that any inter-model set is a model set in some modified cut-and-project scheme with second countable internal space. In both cases, the window in the modified cut-and-project scheme inherits the topological and
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Catalan numbers as discrepancies for a family of substitutions on infinite alphabets Indag. Math. (IF 0.6) Pub Date : 2023-07-07 Dirk Frettlöh, Alexey Garber, Neil Mañibo
In this work, we consider a class of substitutions on infinite alphabets and show that they exhibit a growth behaviour which is impossible for substitutions on finite alphabets. While for both settings the leading term of the tile counting function is exponential (and guided by the inflation factor), the behaviour of the second-order term is strikingly different. For the finite setting, it is known
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Directional ergodicity, weak mixing and mixing for Zd- and Rd-actions Indag. Math. (IF 0.6) Pub Date : 2023-07-07 E. Arthur Robinson, Joseph Rosenblatt, Ayşe A. Şahi̇n
For a measure preserving Zd- or Rd-action T, on a Lebesgue probability space (X,μ), and a linear subspace L⊆Rd, we define notions of direction L ergodicity, weak mixing, and strong mixing. For Rd-actions, it is clear that these direction L properties should correspond to the same properties for the restriction of T to L. But since an arbitrary L⊆Rd does not necessarily correspond to a nontrivial subgroup
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A Carleson type measure and a family of Möbius invariant function spaces Indag. Math. (IF 0.6) Pub Date : 2023-07-07 Guanlong Bao, Fangqin Ye
For 0
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A quantitative Khintchine–Groshev theorem for S-arithmetic diophantine approximation Indag. Math. (IF 0.6) Pub Date : 2023-07-07 Jiyoung Han
In Schmidt (1960), Schmidt studied a quantitative type of Khintchine–Groshev theorem for general (higher) dimensions. Recently, a new proof of the theorem was found, which made it possible to relax the dimensional constraint and more generally, to add on the congruence condition (Alam et al., 2021). In this paper, we generalize this new approach to S-arithmetic spaces and obtain a quantitative version
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Characterisations for uniform amenability Indag. Math. (IF 0.6) Pub Date : 2023-06-24 Jingming Zhu, Jiawen Zhang
In this paper, we provide several characterisations for uniform amenability concerning a family of finitely generated groups. More precisely, we show that the Hulanicki–Reiter condition for uniform amenability can be weakened in several directions, including cardinalities of supports and certain operator norms.
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Harmonic functions for singular quadrant walks Indag. Math. (IF 0.6) Pub Date : 2023-06-17 Viet Hung Hoang, Kilian Raschel, Pierre Tarrago
We consider discrete (time and space) random walks confined to the quarter plane, with jumps only in directions (i,j) with i+j≥0 and small negative jumps, i.e., i,j≥−1. These walks are called singular, and were recently intensively studied from a combinatorial point of view. In this paper, we show how the compensation approach introduced in the 90ies by Adan, Wessels and Zijm may be applied to compute
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On the cycle maximum of birth–death processes and networks of queues Indag. Math. (IF 0.6) Pub Date : 2023-06-08 Richard J. Boucherie
This paper considers the cycle maximum in birth–death processes as a stepping stone to characterisation of the asymptotic behaviour of the maximum number of customers in single queues and open Kelly–Whittle networks of queues. For positive recurrent birth–death processes we show that the sequence of sample maxima is stochastically compact. For transient birth–death processes we show that the sequence
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Approximation by Egyptian fractions and the weak greedy algorithm Indag. Math. (IF 0.6) Pub Date : 2023-06-03 Hùng Việt Chu
Let 0<θ⩽1. A sequence of positive integers (bn)n=1∞ is called a weak greedy approximation of θ if ∑n=1∞1/bn=θ. We introduce the weak greedy approximation algorithm (WGAA), which, for each θ, produces two sequences of positive integers (an) and (bn) such that (a) ∑n=1∞1/bn=θ; (b) 1/an+1<θ−∑i=1n1/bi<1/(an+1−1) for all n⩾1; (c) there exists t⩾1 such that bn/an⩽t infinitely often. We then investigate when