Ezra Waxman

activity

20172026

most citedLower Order Terms for the One-Level Density of a Symplectic Family of Hecke L-Functions

11 citations · 13 across the 9 of their papers we have counts for

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10 papers · 1 filter

math.NT2026

The variance of the number of lattice points in narrow sectors

Stephen Lester, Ezra Waxman, Nadav Yesha

We study the variance of the number of lattice points in smoothed narrow sectors, where the average is taken over the position of the sectors. There are three regimes corresponding…

math.NT2026

Average analytic rank for the $L$ -functions of the elliptic curves $y^{2} = x^{3} - d x$

Chantal David, Lucile Devin, Alessandro Fazzari +1

We study the average analytic rank in the family of $L$ -functions $L (s, E_{d})$ associated with the elliptic curves $E_{d} : y^{2} = x^{3} - d x$ , as $d$ varies over fourth-power-free odd integ…

math.NT2024

One-level densities in families of Grössencharakters associated to CM elliptic curves

Chantal David, Lucile Devin, Ezra Waxman

We study the low-lying zeros of a family of $L$ -functions attached to the CM elliptic curve $E_{d} : y^{2} = x^{3} - d x$ , for each odd and square-free integer $d$ . Specifically, upon…

math.NT2023

On Artin's Primitive Root Conjecture for Function Fields over $F_{q}$

Leonhard Hochfilzer, Ezra Waxman

In 1927, E. Artin proposed a conjecture for the natural density of primes $p$ for which $g$ generates $(Z / p Z)^{\times}$ . By carefully observing numerical deviations…

math.NT2023

On the number of lattice points in thin sectors

Ezra Waxman, Nadav Yesha

On the circle of radius $R$ centred at the origin, consider a ``thin'' sector about the fixed line $y = α x$ with edges given by the lines $y = (α \pm ε) x$ , where $ε= ε_R \rightarro…

math.NT2023

Thue equations over $C (T)$ : The Complete Solution of a Simple quartic family

Bernadette Faye, Ingrid Vukusic, Ezra Waxman +1

In this paper we completely solve a simple quartic family of Thue equations over $C (T)$ . Specifically, we apply the ABC-Theorem to find all solutions $(x,y) \in \mathbb{C}…

math.NT2020

Artin Twin Primes

Magdaléna Tinková, Ezra Waxman, Mikuláš Zindulka

We say that a prime number $p$ is an $Artin prime$ for $g$ if $g$ mod $p$ generates the group $(Z / p Z)^{\times}$ . For appropriately chosen integers $d$ an…

math.NT2019★ 11 cited

Lower Order Terms for the One-Level Density of a Symplectic Family of Hecke L-Functions

Ezra Waxman

In this paper we apply the $L$ -function Ratios Conjecture to compute the one-level density for a symplectic family of $L$ -functions attached to Hecke characters of infinite order.…

math.NT2019★ 2 cited

A Refined Conjecture for the Variance of Gaussian Primes Across Sectors

Ryan C. Chen, Yujin H. Kim, Jared D. Lichtman +6

We derive a refined conjecture for the variance of Gaussian primes across sectors, with a power saving error term, by applying the L-functions Ratios Conjecture. We observe a bifur…

math.NT2017

Angles of Gaussian primes

Zeév Rudnick, Ezra Waxman

Fermat showed that every prime p = 1 mod 4 is a sum of two squares: $p = a^{2} + b^{2}$ . To any of the 8 possible representations (a,b) we associate an angle whose tangent is the ratio…

The variance of the number of lattice points in narrow sectors

Average analytic rank for the L-functions of the elliptic curves y2=x3−dx

One-level densities in families of Grössencharakters associated to CM elliptic curves

On Artin's Primitive Root Conjecture for Function Fields over Fq​

On the number of lattice points in thin sectors

Thue equations over C(T): The Complete Solution of a Simple quartic family

Artin Twin Primes

Lower Order Terms for the One-Level Density of a Symplectic Family of Hecke L-Functions

A Refined Conjecture for the Variance of Gaussian Primes Across Sectors

Angles of Gaussian primes

Average analytic rank for the $L$ -functions of the elliptic curves $y^{2} = x^{3} - d x$

On Artin's Primitive Root Conjecture for Function Fields over $F_{q}$

Thue equations over $C (T)$ : The Complete Solution of a Simple quartic family