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Arithmetic of Hecke L-functions of quadratic extensions of totally real fields J. Number Theory (IF 0.7) Pub Date : 2024-04-21 Marie-Hélène Tomé
Deep work by Shintani in the 1970's describes Hecke -functions associated to narrow ray class group characters of totally real fields in terms of what are now known as Shintani zeta functions. However, for , Shintani's method was ineffective due to its crucial dependence on abstract fundamental domains for the action of totally positive units of on , so-called . These difficulties were recently resolved
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Corrigendum to “Double first moment for [formula omitted] by applying Petersson's formula twice” [J. Number Theory 202 (2019) 141–159] J. Number Theory (IF 0.7) Pub Date : 2024-03-23 Haiwei Sun, Yangbo Ye
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A universal lower bound for certain quadratic integrals of automorphic L–functions J. Number Theory (IF 0.7) Pub Date : 2024-03-21 Laurent Clozel, Peter Sarnak
Let be a cuspidal unitary representation od where denotes the ring of adèles of . Let be its -function. We introduce a universal lower bound for the integral where is equal to 0 or is a zero of on the critical line. In the main text, the proof is given for and under a few assumptions on . It relies on the Mellin transform; the proof involves an extension of a deep result of Friedlander-Iwaniec. An
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Square-free values of random polynomials J. Number Theory (IF 0.7) Pub Date : 2024-03-21 Tim D. Browning, Igor E. Shparlinski
The question of whether or not a given integral polynomial takes infinitely many square-free values has only been addressed unconditionally for polynomials of degree at most 3. We address this question, on average, for polynomials of arbitrary degree.
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Spectrum of all multiplicative functions with application to powerfull numbers J. Number Theory (IF 0.7) Pub Date : 2024-03-21 Tsz Ho Chan
Roughly speaking, the spectrum of multiplicative functions is the set of all possible mean values. In this paper, we are interested in the spectra of multiplicative functions supported over powerfull numbers. We prove that its real logarithmic spectrum takes values from to 1 while it is known that the logarithmic spectrum of real multiplicative functions over all natural numbers takes values from 0
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Relations between values of arithmetic Gevrey series, and applications to values of the Gamma function J. Number Theory (IF 0.7) Pub Date : 2024-03-21 S. Fischler, T. Rivoal
We investigate the relations between the rings , and of values taken at algebraic points by arithmetic Gevrey series of order either −1 (-functions), 0 (analytic continuations of -functions) or 1 (renormalization of divergent series solutions at ∞ of -operators) respectively. We prove in particular that any element of can be written as multivariate polynomial with algebraic coefficients in elements
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Parts in k-indivisible partitions always display biases between residue classes J. Number Theory (IF 0.7) Pub Date : 2024-03-20 Faye Jackson, Misheel Otgonbayar
Let be coprime integers, and let . We let denote the total number of parts among all -indivisible partitions (i.e., those partitions where no part is divisible by ) of which are congruent to modulo . In previous work of the authors , an asymptotic estimate for was shown to exhibit unpredictable biases between congruence classes. In the present paper, we confirm our earlier conjecture in that there
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A note on unlikely intersections in Shimura varieties J. Number Theory (IF 0.7) Pub Date : 2024-03-20 Vahagn Aslanyan, Christopher Daw
We discuss the relationships between the André-Oort, André-Pink-Zannier, and Mordell-Lang conjectures for Shimura varieties. We then combine the latter with the geometric Zilber-Pink conjecture to obtain some new results on unlikely intersections in Shimura varieties.
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Uniform Diophantine approximation with restricted denominators J. Number Theory (IF 0.7) Pub Date : 2024-03-20 Bo Wang, Bing Li, Ruofan Li
Let be an integer and be a strictly increasing subsequence of positive integers with . For each irrational real number , we denote by the supremum of the real numbers for which, for every sufficiently large integer , the equation has a solution with . For every , let () be the set of all real numbers such that () respectively. In this paper, we give some results of the Hausdorfff dimensions of and
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Tempered perfect lattices in the binary case J. Number Theory (IF 0.7) Pub Date : 2024-03-20 Erik Bahnson, Mark McConnell, Kyrie McIntosh
A new algorithm for computing Hecke operators for was introduced in . The algorithm uses , which are certain pairs of lattices together with a quadratic form. These generalize the perfect lattices of Voronoi . The present paper is the first step in characterizing tempered perfect lattices. We obtain a complete classification in the plane, where the Hecke operators are for and its arithmetic subgroups
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First moment of central values of some primitive Dirichlet L-functions with fixed order characters J. Number Theory (IF 0.7) Pub Date : 2024-03-20 Peng Gao, Liangyi Zhao
We evaluate asymptotically the smoothed first moment of central values of families of primitive cubic, quartic and sextic Dirichlet -functions, using the method of double Dirichlet series. Quantitative non-vanishing results for these -values are also proved.
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Fibonacci primes, primes of the form 2n − k and beyond J. Number Theory (IF 0.7) Pub Date : 2024-03-20 Jon Grantham, Andrew Granville
We speculate on the distribution of primes in exponentially growing, linear recurrence sequences in the integers. By tweaking a heuristic which is successfully used to predict the number of prime values of polynomials, we guess that either there are only finitely many primes , or else there exists a constant (which we can give good approximations to) such that there are primes with , as . We compare
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A zero-sum problem related to the max gap of the unit group of the residue class ring J. Number Theory (IF 0.7) Pub Date : 2024-03-20 Xiao Jiang, Wenkai Yang
Let be a sequence over a finite abelian group and be the times that occurs in . A sequence over is called weak-regular if for every . Denote by the smallest integer such that every weak-regular sequence over of length has a nonempty zero-sum subsequence of satisfying for some . has been formulated by Gao et al. very recently to study zero-sum problems in a unify way and determined only for cyclic groups
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Shifted convolution sums of divisor functions with Fourier coefficients J. Number Theory (IF 0.7) Pub Date : 2024-03-20 Miao Lou
Let be a holomorphic cusp form of weight for the full modular group . Denote its -th normalized Fourier coefficient by . Let denote that -th divisor function with . In this paper, we consider the shifted convolution sum We succeed in obtaining a non-trivial upper bound, which is uniform in the shift parameter .
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Finding Galois splitting models to compute local invariants J. Number Theory (IF 0.7) Pub Date : 2024-03-19 Benjamin Carrillo
For prime and small , Jones and Roberts have developed a database recording invariants for -adic extensions of degree . We contributed to this database by computing the Galois slope content, Galois mean slope, and inertia subgroup for a variety of wildly ramified extensions of composite degree using the idea of . We will describe a number of strategies to find Galois splitting models including an original
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Shifted convolution sum with weighted average: GL(3)×GL(3) setup J. Number Theory (IF 0.7) Pub Date : 2024-03-19 Mohd Harun, Saurabh Kumar Singh
This article will prove non-trivial estimates for the average and weighted average version of general shifted convolution sums by using the circle method.
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Klingen vectors for depth zero supercuspidals of GSp(4) J. Number Theory (IF 0.7) Pub Date : 2024-03-19 Jonathan Cohen
Let be a non-archimedean local field of characteristic zero and a depth zero, irreducible, supercuspidal representation of . We calculate the dimensions of the spaces of Klingen-invariant vectors in of level for all .
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Hausdorff dimension of certain sets related to random αβ-orbits which are not dense J. Number Theory (IF 0.7) Pub Date : 2024-03-19 Liuqing Peng, Jun Wu, Jian Xu
Let such that at least one of them is irrational. It is known that the random -orbits of the Bernoulli mixture of rotations of and by choosing them with equal probability are uniformly distributed modulo 1 with probability one. Chen et al. (2021) showed that the exceptional set in the probability space has full Hausdorff dimension. In this note, we prove that certain sets related to random -orbits
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On Cilleruelo-Nathanson's method in Sidon sets J. Number Theory (IF 0.7) Pub Date : 2024-03-19 Jin-Hui Fang
For nonnegative integers with , a set of nonnegative integers is defined as a sequence if, for every nonnegative integer , the number of representations of with the form is no larger than , where and for . Let be the set of integers and be the set of positive integers. In 2013, by introducing the method of , Cilleruelo and Nathanson obtained the following result: let be any function such that and let
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Finite flat group schemes over Z killed by 19 J. Number Theory (IF 0.7) Pub Date : 2024-03-18 Lassina Dembélé, René Schoof
Since simple commutative finite flat group schemes over are killed by a prime number , their order is a power of . Abraškin and Fontaine have both shown that for primes the only simple -power order group schemes are and . We extend their result to .
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Corrigendum to “On p-adic Siegel Eisenstein series” [J. Number Theory 251 (2023) 3–30] J. Number Theory (IF 0.7) Pub Date : 2024-02-26 H. Katsurada, S. Nagaoka
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Algebraicity modulo p of generalized hypergeometric series [formula omitted] J. Number Theory (IF 0.7) Pub Date : 2024-02-21 D, a, n, i, e, l, , V, a, r, g, a, s, -, M, o, n, t, o, y, a
Let be the hypergeometric series with parameters and in , let be the least common multiple of the denominators of , written in lowest form and let be a prime number such that does not divide and . Recently in , it was shown that if for all , then the reduction of modulo is algebraic over . A standard way to measure the complexity of an algebraic power series is to estimate its degree and its height
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On integral class field theory for varieties over p-adic fields J. Number Theory (IF 0.7) Pub Date : 2024-02-20 Thomas H. Geisser, Baptiste Morin
Let be a finite extension of the -adic numbers with ring of integers and residue field . Let a regular scheme, proper, flat, and geometrically irreducible over of dimension , and its generic fiber. We show, under some assumptions on , that there is a reciprocity isomorphism of locally compact groups from the cohomology theory defined in to an integral model of the abelianized fundamental group . After
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The finitude of tamely ramified pro-p extensions of number fields with cyclic p-class groups J. Number Theory (IF 0.7) Pub Date : 2024-02-20 Yoonjin Lee, Donghyeok Lim
Let be an odd prime and be a number field whose -class group is cyclic. Let be the maximal pro- extension of which is unramified outside a single non--adic prime ideal of . In this work, we study the finitude of the Galois group of over . We prove that is finite for the majority of 's such that the generator rank of is two, provided that for , is not a complex quartic field containing the primitive
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Rational self-maps with a regular iterate on a semiabelian variety J. Number Theory (IF 0.7) Pub Date : 2024-02-20 Jason Bell, Dragos Ghioca, Zinovy Reichstein
Let be a semiabelian variety defined over an algebraically closed field of characteristic 0. Let be a dominant rational self-map. Assume that an iterate is regular for some and that there exists no non-constant homomorphism of semiabelian varieties such that for some . We show that under these assumptions Φ itself must be a regular. We also prove a variant of this assertion in prime characteristic
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Higher order Turán inequalities for the distinct partition function J. Number Theory (IF 0.7) Pub Date : 2024-02-20 Janet J.W. Dong, Kathy Q. Ji
We prove that the number of partitions of with distinct parts is log-concave for and satisfies the third-order Turán inequalities for conjectured by Craig and Pun. In doing so, we establish explicit error terms for and for based on Chern's asymptotic formulas for -quotients.
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Divisibility properties of polynomial expressions of random integers J. Number Theory (IF 0.7) Pub Date : 2024-02-20 Zakhar Kabluchko, Alexander Marynych
We study divisibility properties of a set , where are polynomials in variables over and is a point picked uniformly at random from the set . We show that, as , the GCD and the suitably normalized LCM of this set converge in distribution to a.s. finite random variables under mild assumptions on . Our approach is based on the known fact that the uniform distribution on converges to the Haar measure on
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Bounds for the quartic Weyl sum J. Number Theory (IF 0.7) Pub Date : 2024-02-20 D, ., R, ., , H, e, a, t, h, -, B, r, o, w, n
We improve the standard Weyl estimate for quartic exponential sums in which the argument is a quadratic irrational. Specifically we show that for any and any quadratic irrational . Classically one would have had the exponent for such . In contrast to the author's earlier work on cubic Weyl sums (which was conditional on the -conjecture), we show that the van der Corput -steps are sufficient for the
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Shifted convolution sums motivated by string theory J. Number Theory (IF 0.7) Pub Date : 2024-02-20 Ksenia Fedosova, Kim Klinger-Logan
In , it was conjectured that a particular shifted sum of even divisor sums vanishes, and in , a formal argument was given for this vanishing. Shifted convolution sums of this form appear when computing the Fourier expansion of coefficients for the low energy scattering amplitudes in type IIB string theory and have applications to subconvexity bounds of -functions. In this article, we generalize the
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Mod-p Galois representations not arising from abelian varieties J. Number Theory (IF 0.7) Pub Date : 2024-02-20 S, h, i, v, a, , C, h, i, d, a, m, b, a, r, a, m
It is known that any Galois representation with determinant equal to the mod- cyclotomic character, arises from the -torsion of an elliptic curve over , if and only if . In dimension , when , it is again known that any Galois representation valued in with cyclotomic similitude character arises from an abelian surface. In this paper, we study this question for all primes and dimensions . When and ,
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Eventual log-concavity of k-rank statistics for integer partitions J. Number Theory (IF 0.7) Pub Date : 2024-02-20 N, i, a, n, , H, o, n, g, , Z, h, o, u
Let denote the number of partitions of with Garvan -rank . It is well-known that Andrews–Garvan–Dyson's crank and Dyson's rank are the -rank for and , respectively. In this paper, we prove that the sequences are log-concave for all sufficiently large integers and each integer . In particular, we partially solve the log-concavity conjecture for Andrews–Garvan–Dyson's crank and Dyson's rank, which was
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On a Ramanujan-type series associated with the Heegner number 163 J. Number Theory (IF 0.7) Pub Date : 2024-02-20 J, o, h, n, , M, ., , C, a, m, p, b, e, l, l
Using the Wolfram package and the command, together with numerical estimates involving the elliptic lambda and elliptic alpha functions, Bagis and Glasser, in 2013, introduced a conjectural Ramanujan-type series related to the class number for a quadratic form with discriminant . This conjectured series is of level one and has positive terms, and recalls the Chudnovsky brothers' alternating series
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Numerically explicit estimates for the distribution of rough numbers J. Number Theory (IF 0.7) Pub Date : 2024-02-20 Kai Fan
For and , let denote the number of positive integers up to free of prime divisors less than or equal to . In 1950 de Bruijn studied the approximation of by the quantity where is Euler's constant and He showed that the asymptotic formula holds uniformly for all , where is a positive decreasing function related to the error estimates in the Prime Number Theorem. In this paper we obtain numerically explicit
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The pair correlation function of multi-dimensional low-discrepancy sequences with small stochastic error terms J. Number Theory (IF 0.7) Pub Date : 2024-02-20 Anja Schmiedt, Christian Weiß
In any dimension , there is no known example of a low-discrepancy sequence which possesses Poisssonian pair correlations. This is in some sense rather surprising, because low-discrepancy sequences always have -Poissonian pair correlations for all and are therefore arbitrarily close to having Poissonian pair correlations (which corresponds to the case ). In this paper, we further elaborate on the closeness
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Residue of special functions of Anderson A-modules at the characteristic graph J. Number Theory (IF 0.7) Pub Date : 2024-02-20 Quentin Gazda, Andreas Maurischat
Let be an Anderson -module over . The period lattice of is related to its module of special functions by means of a non-canonical isomorphism introduced by the authors in . In this paper, we explain how a modification of the inverse map is canonical by interpreting it as a residue morphism along the characteristic graph. This phenomenon has already been observed in various situations. The main innovation
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A note on Galois groups of linearized polynomials J. Number Theory (IF 0.7) Pub Date : 2024-02-19 P, e, t, e, r, , M, ü, l, l, e, r
Let be a monic -linearized polynomial over of degree , where is an odd prime. In , Gow and McGuire showed that the Galois group of over the field of rational functions is unless . The case of even remained open, but it was conjectured that the result holds too and partial results were given. In this note we settle this conjecture. In fact we use Hensel's Lemma to give a unified proof for all prime
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The resolution of three exponential Diophantine equations in several variables J. Number Theory (IF 0.7) Pub Date : 2024-02-19 Csanád Bertók, Lajos Hajdu
We find all solutions of three exponential Diophantine equations, arising from certain quadratic, cubic and quartic identities. The first identity comes from a painting of the famous Russian painter Nikolay Bogdanov-Belsky, highlighted by Ja. I. Perelman. The equations have five, four and six terms, respectively, so they cannot be handled by classical tools based upon Baker's method. To solve the equations
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Lie invariant Frobenius lifts J. Number Theory (IF 0.7) Pub Date : 2024-02-19 A, l, e, x, a, n, d, r, u, , B, u, i, u, m
We begin with the observation that the -adic completion of any affine elliptic curve with ordinary reduction possesses Frobenius lifts that are “Lie invariant mod ” in the sense that the “normalized” action of on 1-forms preserves mod the space of invariant 1-forms. Our main result is that, after removing the 2-torsion sections, the above situation can be “infinitesimally deformed” in the sense that
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Sato–Tate type distributions for matrix points on elliptic curves and some K3 surfaces J. Number Theory (IF 0.7) Pub Date : 2024-02-19 Avalon Blaser, Molly Bradley, Daniel A.N. Vargas, Kathy Xing
Generalizing the problem of counting rational points on curves and surfaces over finite fields, we consider the setting of matrix points with finite field entries. We obtain exact formulas for matrix point counts on elliptic curves and certain 3 surfaces for “supersingular” primes. These exact formulas, which involve partitions of integers up to , essentially coincide with the expected value for the
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Quotients of the Bruhat-Tits tree by function field analogs of the Hecke congruence subgroups J. Number Theory (IF 0.7) Pub Date : 2024-02-08 C, l, a, u, d, i, o, , B, r, a, v, o
Let be a smooth, projective and geometrically integral curve defined over a finite field . For each closed point of , let be the ring of functions that are regular outside , and let be the completion at of the function field of . In order to study groups of the form , Serre describes the quotient graph , where is the Bruhat-Tits tree defined from .
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Computations on overconvergence rates related to the Eisenstein family J. Number Theory (IF 0.7) Pub Date : 2024-01-24 B, r, y, a, n, , A, d, v, o, c, a, a, t
We provide for primes a method to compute valuations appearing in the “formal” Katz expansion of the family derived from the family of Eisenstein series . We will describe two algorithms: the first one to compute the Katz expansion of an overconvergent modular form and the second one, which uses the first algorithm, to compute valuations appearing in the “formal” Katz expansion. Based on data obtained
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The number of preimages of iterates of ϕ and σ J. Number Theory (IF 0.7) Pub Date : 2024-01-24 A, g, b, o, l, a, d, e, , A, k, a, n, d, e
Paul Erdos and Carl Pomerance have proofs on an asymptotic upper bound on the number of preimages of Euler's totient function and the sum-of-divisors functions . In this paper, we will extend the upper bound to the number of preimages of iterates of and . Using these new asymptotic upper bounds, a conjecture in de Koninck and Kátai's paper, “On the uniform distribution of certain sequences involving
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Quartic integral polynomial Pell equations J. Number Theory (IF 0.7) Pub Date : 2024-01-24 Zachary Scherr, Katherine Thompson
In this paper we classify all monic, quartic, polynomials for which the Pell equation has a non-trivial solution with .
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On certain kernel functions and shifted convolution sums of the Fourier coefficients J. Number Theory (IF 0.7) Pub Date : 2024-01-22 Kampamolla Venkatasubbareddy, Ayyadurai Sankaranarayanan
We study the behavior of the shifted convolution sum involving even power of the Fourier coefficients of holomorphic cusp forms with a weight function to be the k-full kernel function for any fixed integer k≥2.
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Functional equations and gamma factors of local zeta functions for the metaplectic cover of SL2 J. Number Theory (IF 0.7) Pub Date : 2024-01-23 Kazuki Oshita, Masao Tsuzuki
We introduce a local zeta-function for an irreducible admissible supercuspidal representation of the metaplectic double cover of over a non-archimedean local field of characteristic zero. We prove a functional equation of the local zeta-functions showing that the gamma factor is given by a Mellin type transform of the Bessel function of . We obtain an expression of the gamma factor, which shows its
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On quotients of derivatives of L-functions inside the critical strip J. Number Theory (IF 0.7) Pub Date : 2024-01-22 R, a, s, h, i, , L, u, n, i, a
In , Gun, Murty and Rath studied non-vanishing and transcendental nature of special values of a varying class of -functions and their derivatives. This led to a number of works by several authors in different set-ups including studying higher derivatives. However, all these works were focused around the central point of the critical strip. In this article, we extend the study to arbitrary points in
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Sparse sets that satisfy the prime number theorem J. Number Theory (IF 0.7) Pub Date : 2024-01-22 Olivier Bordellès, Randell Heyman, Dion Nikolic
For arbitrary real we examine the set . Asymptotic formulas for the cardinality of this set and the number of primes in this set are given. The prime counting result uses an alternate Vaughan's decomposition for the von Mangoldt function, with triple exponential sums instead of double exponential sums. These sets are the sparsest known sets that satisfy the prime number theorem, in the sense that the
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Universal sums of triangular numbers and squares J. Number Theory (IF 0.7) Pub Date : 2024-01-22 Z, i, c, h, e, n, , Y, a, n, g
In this paper, we study universal sums of triangular numbers and squares. Specifically, we prove that a sum of triangular numbers and squares is universal if and only if it represents , and 48.
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The factorial function and generalizations, extended J. Number Theory (IF 0.7) Pub Date : 2024-01-22 Jeffrey C. Lagarias, Wijit Yangjit
This paper presents an extension of Bhargava's theory of factorials associated to any nonempty subset of . Bhargava's factorials are invariants, constructed using the notion of -orderings of where is a prime. This paper defines -orderings of any nonempty subset of for all integers , as well as “extreme” cases and . It defines generalized factorials and generalized binomial coefficients as nonnegative
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One-level density of zeros of Dirichlet L-functions over function fields J. Number Theory (IF 0.7) Pub Date : 2024-01-08 Hua Lin
Text We compute the one-level density of zeros of order ℓ Dirichlet L-functions over function fields Fq[t] for ℓ=3,4 in the Kummer setting (q≡1(modℓ)) and for ℓ=3,4,6 in the non-Kummer setting (q≢1(modℓ)). In each case, we obtain a main term predicted by Random Matrix Theory (RMT) and lower order terms not predicted by RMT. We also confirm the symmetry type of the families is unitary, supporting Katz
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Collision of orbits for a one-parameter family of Drinfeld modules J. Number Theory (IF 0.7) Pub Date : 2023-12-28 Dragos Ghioca
We prove a result (see Theorem 1.1) regarding unlikely intersections of orbits for a given 1-parameter family of Drinfeld modules. We also advance a couple of general conjectures regarding unlikely intersections for algebraic families of Drinfeld modules (see Conjecture 1.3, Conjecture 2.3).
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On the variance of the Fibonacci partition function J. Number Theory (IF 0.7) Pub Date : 2023-12-28 Sam Chow, Owen Jones
We determine the order of magnitude of the variance of the Fibonacci partition function. The answer is different to the most naive guess. The proof involves a diophantine system and an inhomogeneous linear recurrence.
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On integers of the form p+2k1r1+⋯+2ktrt J. Number Theory (IF 0.7) Pub Date : 2023-12-29 Yong-Gao Chen, Ji-Zhen Xu
Let r1,…,rt be positive integers and let R2(r1,…,rt) be the set of positive odd integers that can be represented as p+2k1r1+⋯+2ktrt, where p is a prime and k1,…,kt are positive integers. It is easy to see that if r1−1+⋯+rt−1<1, then the set R2(r1,…,rt) has asymptotic density zero. In this paper, we prove that if r1−1+⋯+rt−1≥1, then the set R2(r1,…,rt) has a positive lower asymptotic density. Several
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Mean of the product of derivatives of Hardy's Z-function with Dirichlet polynomial J. Number Theory (IF 0.7) Pub Date : 2023-12-29 Mithun Kumar Das, Sudhir Pujahari
Inspired by the work of Balasubramanian, Conrey and Heath-Brown [1], we obtain an asymptotic expression for the mean of the product of any two finite order derivatives of Hardy's Z-function times Dirichlet polynomials in short intervals.
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On real zeros of the Hurwitz zeta function J. Number Theory (IF 0.7) Pub Date : 2023-12-29 Karin Ikeda
In this paper, we present results on the uniqueness of the real zeros of the Hurwitz zeta function in given intervals. The uniqueness in question, if the zeros exist, has already been proved for the intervals (0,1) and (−N,−N+1) for N≥5 by Endo-Suzuki and Matsusaka, respectively. We prove the uniqueness of the real zeros in the remaining intervals by examining the behavior of certain associated polynomials
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Moments of ideal class counting functions J. Number Theory (IF 0.7) Pub Date : 2023-12-29 Kam Cheong Au
We consider the counting function of ideals in a given ideal class of a number field of degree d. This describes, at least conjecturally, the Fourier coefficients of an automorphic form on GL(d), typically not a Hecke eigenform and not cuspidal. We compute its moments, and also investigate the moments of the corresponding cuspidal projection.
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Class numbers of multinorm-one tori J. Number Theory (IF 0.7) Pub Date : 2023-12-29 Fan-Yun Hung, Chia-Fu Yu
We present a formula for the class number of a multinorm one torus TL/k associated to any étale algebra L over a global field k. This is deduced from a formula for analogues of invariants introduced by T. Ono, which are interpreted as a generalization of Gauss genus theory. This paper includes the variants of Ono's invariant for arbitrary S-ideal class numbers and the narrow version, generalizing results
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A basis for the space of weakly holomorphic Drinfeld modular forms of level T J. Number Theory (IF 0.7) Pub Date : 2023-12-28 Tarun Dalal
In this article, we explicitly construct a canonical basis for the space of certain weakly holomorphic Drinfeld modular forms for Γ0(T) (resp., for Γ0+(T)) and compute the generating function satisfied by the basis elements. We also give an explicit expression for the action of the Θ-operator, which depends on the divisor of meromorphic Drinfeld modular forms.