L. Bary‐Soroker

activity

20052026

most citedShifted convolution and the Titchmarsh divisor problem over F_q[t]

41 citations · 180 across the 49 of their papers we have counts for

collaborators

55 papers

math.NT2026

Generic Manin-Mumford

Lior Bary-Soroker, Borys Kadets

Given a collection of algebraic numbers $S \subset Q$ we study the varieties $V$ in $A_{C}^{m}$ such that $V(\mathbb{C})\cap\mathcal{S}^m…

math.NT2025★ 1 cited

Irreducibility of the characteristic polynomials of random tridiagonal matrices

Lior Bary-Soroker, Daniele Garzoni, Sasha Sodin

Conditionally on the Riemann hypothesis for certain Dedekind zeta functions, we show that the characteristic polynomial of a class of random tridiagonal matrices of large dimension…

math.NT2024

Irreducibility of Polynomials with Square Coefficients over Finite Fields

Lior Bary-Soroker, Roy Shmueli

We study a random polynomial of degree $n$ over the finite field $F_{q}$ , where the coefficients are independent and identically distributed and uniformly chosen from the sq…

math.NT2024

On the irreducibility of $f (2^{n}, 3^{m}, X)$ and other such polynomials

Lior Bary-Soroker, Daniele Garzoni, Vlad Matei

Let $f (t_{1}, \dots, t_{r}, X) \in Z [t_{1}, \dots, t_{r}, X]$ be irreducible and let $a_{1}, \dots, a_{r} \in Z ∖ {0, \pm 1}$ . Under a necessary ramification as…

math.NT2024

Full Galois groups of polynomials with slowly growing coefficients

Lior Bary-Soroker, Noam Goldgraber

Choose a polynomial $f$ uniformly at random from the set of all monic polynomials of degree $n$ with integer coefficients in the box $[- L, L]^{n}$ . The main result of the paper assert…

math.NT2023

Hilbert properties under base change in small extensions

Lior Bary-Soroker, Arno Fehm, Sebastian Petersen

We study the preservation of the Hilbert property and of the weak Hilbert property under base change in field extensions. In particular we show that these properties are preserved…

math.NT2023

Product Sets of Arithmetic Progressions in Function Fields

Lior Bary-Soroker, Noam Goldgraber

We study product sets of finite arithmetic progressions of polynomials over a finite field. We prove a lower bound for the size of the product set, uniform in a wide range of param…

math.NT2023

Irreducibility of Littlewood polynomials of special degrees

Lior Bary-Soroker, David Hokken, Gady Kozma +1

Let $f$ be sampled uniformly at random from the set of degree $n$ polynomials whose coefficients lie in ${\pm 1}$ . A folklore conjecture, known to hold under GRH, states that th…

math.NT2023★ 3 cited

Galois groups of random additive polynomials

Lior Bary-Soroker, Alexei Entin, Eilidh McKemmie

We study the distribution of the Galois group of a random $q$ -additive polynomial over a rational function field: For $q$ a power of a prime $p$ , let $f=X^{q^n}+a_{n-1}X^{q^{n-1}}+…

math.NT2022

Probabilistic Galois Theory -- The Square Discriminant Case

Lior Bary-Soroker, Or Ben-Porath, Vlad Matei

The paper studies the probability for a Galois group of a random polynomial to be $A_{n}$ . We focus on the so-called large box model, where we choose the coefficients of the polynomi…

math.NT2022

Ramified covers of abelian varieties over torsion fields

Lior Bary-Soroker, Arno Fehm, Sebastian Petersen

We study rational points on ramified covers of abelian varieties over certain infinite Galois extensions of $Q$ . In particular, we prove that every elliptic curve $E$ over…

math.NT2022

Hilbert's irreducibility theorem via random walks

Lior Bary-Soroker, Daniele Garzoni

Let $G$ be a connected linear algebraic group over a number field $K$ , let $Γ$ be a finitely generated Zariski dense subgroup of $G (K)$ and let $Z \subseteq G (K)$ be a thin set, in…

math.NT2021

The minimal ramification problem for rational function fields over finite fields

Lior Bary-Soroker, Alexei Entin, Arno Fehm

We study the minimal number of ramified primes in Galois extensions of rational function fields over finite fields with prescribed finite Galois group. In particular, we obtain a g…

math.NT2020

On the Galois Theory of Generalized Laguerre Polynomials and Trimmed Exponential

Lior Bary-Soroker, Or Ben-Porath

Inspired by the work of Schur on the Taylor series of the exponential and Laguerre polynomials, we study the Galois theory of trimmed exponentials $f_{n,n+k}=\sum_{i=0}^{k} \frac{x…

math.NT2020★ 20 cited

Irreducibility of random polynomials: general measures

Lior Bary-Soroker, Dimitris Koukoulopoulos, Gady Kozma

Let $μ$ be a probability measure on $Z$ that is not a Dirac mass and that has finite support. We prove that if the coefficients of a monic polynomial $f(x)\in\mathbb{Z}[x]…

math.NT2019

Explicit Hilbert's Irreducibility Theorem in Function Fields

Lior Bary-Soroker, Alexei Entin

We prove a quantitative version of Hilbert's irreducibility theorem for function fields: If $f (T_{1}, \dots, T_{n}, X)$ is an irreducible polynomial over the field of rational functions…

math.NT2018★ 4 cited

Chebotarev density theorem in short intervals for extensions of $F_{q} (T)$

Lior Bary-Soroker, Ofir Gorodetsky, Taelin Karidi +1

An old open problem in number theory is whether Chebotarev density theorem holds in short intervals. More precisely, given a Galois extension $E$ of $Q$ with Galois group…

math.PR2018★ 1 cited

Supplement to the article "irreducible polynomials with bounded height"

Lior Bary-Soroker, Gady Kozma

We show that the determinant of a random matrix is unlikely to be a square.

math.NT2018★ 4 cited

Roots of Polynomials and The Derangement Problem

Lior Bary-Soroker, Ofir Gorodetsky

We present a new killing-a-fly-with-a-sledgehammer proof of one of the oldest results in probability which says that the probability that a random permutation on $n$ elements has n…

math.NT2017

On the distribution of the rational points on cyclic covers in the absence of roots of unity

Lior Bary-Soroker, Patrick Meisner

In this paper we study the number of rational points on curves in an ensemble of abelian covers of the projective line: Let $ℓ$ be a prime, $q$ a prime power and consider the en…

math.NT2017★ 1 cited

Cubic twin prime polynomials are counted by a modular form

Lior Bary-Soroker, Jakob Stix

We present the geometry lying behind counting twin prime polynomials in $F_{q} [T]$ in general. We compute cohomology and explicitly count points by means of a twisted Lefsch…

math.NT2017★ 28 cited

Irreducible polynomials of bounded height

Lior Bary-Soroker, Gady Kozma

The goal of this paper is to prove that a random polynomial with i.i.d. random coefficients taking values uniformly in ${1, \dots, 210}$ is irreducible with probability tending t…

math.NT2017

Correlations of sums of two squares and other arithmetic functions in function fields

Lior Bary-Soroker, Arno Fehm

We investigate a function field analogue of a recent conjecture on autocorrelations of sums of two squares by Freiberg, Kurlberg and Rosenzweig, which generalizes an older conjectu…

math.NT2016★ 6 cited

Sieves and the Minimal Ramification Problem

Lior Bary-Soroker, Tomer M. Schlank

The minimal ramification problem may be considered as a quantitative version of the inverse Galois problem. For a nontrivial finite group $G$ , let $m (G)$ be the minimal integer $m$ …

Generic Manin-Mumford

Irreducibility of the characteristic polynomials of random tridiagonal matrices

Irreducibility of Polynomials with Square Coefficients over Finite Fields

On the irreducibility of f(2n,3m,X) and other such polynomials

Full Galois groups of polynomials with slowly growing coefficients

Hilbert properties under base change in small extensions

Product Sets of Arithmetic Progressions in Function Fields

Irreducibility of Littlewood polynomials of special degrees

Galois groups of random additive polynomials

Probabilistic Galois Theory -- The Square Discriminant Case

Ramified covers of abelian varieties over torsion fields

Hilbert's irreducibility theorem via random walks

The minimal ramification problem for rational function fields over finite fields

On the Galois Theory of Generalized Laguerre Polynomials and Trimmed Exponential

Irreducibility of random polynomials: general measures

Explicit Hilbert's Irreducibility Theorem in Function Fields

Chebotarev density theorem in short intervals for extensions of Fq​(T)

Supplement to the article "irreducible polynomials with bounded height"

Roots of Polynomials and The Derangement Problem

On the distribution of the rational points on cyclic covers in the absence of roots of unity

Cubic twin prime polynomials are counted by a modular form

Irreducible polynomials of bounded height

Correlations of sums of two squares and other arithmetic functions in function fields

Sieves and the Minimal Ramification Problem

On the irreducibility of $f (2^{n}, 3^{m}, X)$ and other such polynomials

Chebotarev density theorem in short intervals for extensions of $F_{q} (T)$