HUN-REN Alfréd Rényi Institute of Mathematics

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19942026

most citedBrownian distance covariance

857 citations

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54 papers · 1 filter

math.NT2026

Short intervals for the Romanoff-type sumset

Yuchen Ding, Johann Verwee

Let $X$ be large and let $P$ denote the set of primes. Fix positive real parameters $r_{1}, \dots, r_{s}$ and a parameter $λ ⩾ 1$ determined by a balancing relation, and…

math.NT2024★ 2 cited

Difference sets and positive exponential sums II: cubic residues in cyclic groups

Mate Matolcsi, Imre Z. Ruzsa

By constructing suitable nonnegative exponential sums we give upper bounds on the cardinality of any set $B_{q}$ in cyclic groups $\ZZ_q$ such that the difference set $B_{q} - B_{q}$ avoid…

math.NT2024★ 1 cited

Local square mean in the hyperbolic circle problem

András Biró

Let $Γ \subseteq P S L_{2} (R)$ be a finite volume Fuchsian group. The hyperbolic circle problem is the estimation of the number of elements of the $Γ$ -orbit of $z$ in a hyperbolic…

math.NT2024

On an estimate on Götzky's domain

Dávid Tóth

A fundamental domain $F \subset H^{2}$ for the Hilbert modular group belonging to the quadratic number field $Q (5)$ was constructed by Götzky almost a hundred years ago. He als…

math.NT2023★ 2 cited

The Prime Geodesic Theorem in Arithmetic Progressions

Dimitrios Chatzakos, Gergely Harcos, Ikuya Kaneko

We address the prime geodesic theorem in arithmetic progressions, and resolve conjectures of Golovchanski\uı-Smotrov (1999). In particular, we prove that the traces of closed geode…

math.NT2023

On the geometric trace of a generalized Selberg trace formula

András Biró, Dávid Tóth

A certain generalization of the Selberg trace formula was proved by the first named author in 1999. In this generalization instead of considering the integral of $K (z, z)$ (where $K…

math.NT2023★ 1 cited

Some examples of well-behaved Beurling number systems

Frederik Broucke, Gregory Debruyne, Szilárd Révész

We investigate the existence of well-behaved Beurling number systems, which are systems of Beurling generalized primes and integers which admit a power saving in the error term of…

math.NT2023★ 3 cited

A new zero-free region for Rankin-Selberg $L$ -functions

Gergely Harcos, Jesse Thorner

Let $π$ and $π^{'}$ be cuspidal automorphic representations of $GL (n)$ and $GL (n^{'})$ with unitary central characters. We establish a new zero-free region for all $\ma…

math.NT2022★ 1 cited

A supplement to Chebotarev's density theorem

Gergely Harcos, Kannan Soundararajan

Let $L / K$ be a Galois extension of number fields with Galois group $G$ . We show that if the density of prime ideals in $K$ that split totally in $L$ tends to $1/∣ G ∣$ with a power s…

math.NT2022★ 1 cited

On the sequence $n! mod p$

A. Grebennikov, A. Sagdeev, A. Semchankau +1

We prove, that the sequence $1!, 2!, 3!, \dots$ produces at least $(2 + o (1)) p$ distinct residues modulo prime $p$ . Moreover, factorials on an interval $\mathcal{I} \…

math.NT2021★ 4 cited

A Riemann-von Mangoldt-type formula for the distribution of Beurling primes

Szilárd Gy. Révész

In this paper we work out a Riemann-von Mangoldt type formula for the summatory function $ψ (x) := \sum_{g \in G, ∣ g ∣ \leq x} Λ_{G} (g)$ , where $G$ is an arithmetical semigroup (a Beurlin…

math.NT2021★ 4 cited

Beyond the spherical sup-norm problem

Valentin Blomer, Gergely Harcos, Péter Maga +1

We open a new perspective on the sup-norm problem and propose a version for non-spherical Maass forms when the maximal compact K is non-abelian and the dimension of the K-type gets…

math.NT2021★ 7 cited

Maximizing Sudler products via Ostrowski expansions and cotangent sums

Christoph Aistleitner, Bence Borda

There is an extensive literature on the asymptotic order of Sudler's trigonometric product $P_{N} (α) = \prod_{n = 1}^{N} ∣2 sin (π n α) ∣$ for fixed or for "typical" values of $α$ . In th…

math.NT2020★ 7 cited

Distribution of Beurling primes and zeroes of the Beurling zeta function I. Distribution of the zeroes of the zeta function of Beurling

Szilárd Gy. Révész

We prove three results on the density resp. local density and clustering of zeros of the Beurling zeta function $ζ (s)$ close to the one-line $σ := ℜ s = 1$ . The analysis here brings…

math.NT2020★ 4 cited

The density hypothesis for horizontal families of lattices

Mikołaj Frączyk, Gergely Harcos, Péter Maga +1

We prove the density hypothesis for wide families of arithmetic orbifolds arising from all division quaternion algebras over all number fields of bounded degree. Our power-saving b…

math.NT2019★ 4 cited

On the discrepancy of random subsequences of ${n α}$

Istvan Berkes, Bence Borda

For irrational $α$ , ${n α}$ is uniformly distributed mod 1 in the Weyl sense, and the asymptotic behavior of its discrepancy is completely known. In contrast, very few precise res…

math.NT2019

Counting bounded elements of a number field

Mikołaj Frączyk, Gergely Harcos, Péter Maga

We estimate, in a number field, the number of elements and the maximal number of linearly independent elements, with prescribed bounds on their valuations. As a by-product, we obta…

math.NT2019★ 5 cited

On Kuznetsov-Bykovskii's formula of counting prime geodesics

Giacomo Cherubini, Han Wu, Gergely Zábrádi

We generalize a formula on the counting of prime geodesics, due to Kuznetsov-Bykovskii, used in the work of Soundararajan-Young on the prime geodesic theorem. The method works over…

math.NT2018★ 14 cited

The prime geodesic theorem in square mean

Antal Balog, András Biró, Gergely Harcos +1

We strengthen the recent result of Cherubini and Guerreiro on the square mean of the error term in the prime geodesic theorem for $PSL_{2} (Z)$ . We also develop a sh…

math.NT2018★ 4 cited

On iterated product sets with shifts

Brandon Hanson, Oliver Roche-Newton, Dmitrii Zhelezov

We prove that, for any finite set $A \subset Q$ with $∣ AA ∣ \leq K ∣ A ∣$ and any positive integer $k$ , the $k$ -fold product set of the shift $A + 1$ satisfies the bound $$| \{(a…

math.NT2017★ 5 cited

Estimating the greatest common divisor of the value of two polynomials

Péter E. Frenkel, Gergely Zábrádi

Let $p$ be a fixed prime, and let $v (a)$ stand for the exponent of $p$ in the prime factorization of the integer $a$ . Let $f$ and $g$ be two monic polynomials with integer coeffici…

math.NT2017★ 7 cited

Analytic properties of spherical cusp forms on GL(n)

Valentin Blomer, Gergely Harcos, Péter Maga

Let $ϕ$ be an $L^{2}$ -normalized spherical vector in an everywhere unramified cuspidal automorphic representation of $PGL_{n}$ over $Q$ with Laplace eigenvalue $λ_{ϕ}$ .…

math.NT2017

Average Goldbach and the Quasi-Riemann Hypothesis

Gautami Bhowmik, Imre Z. Ruzsa

We prove that a good average order on the Goldbach generating function implies that the real parts of the non-trivial zeros of the Riemann zeta function are strictly less than 1. T…

math.NT2017★ 4 cited

On the global sup-norm of GL(3) cusp forms