Alexei Entin

activity

20112024

most citedOn the Bateman-Horn conjecture for polynomials over large finite fields

18 citations · 25 across the 18 of their papers we have counts for

collaborators

Showing 2023Show all

3 papers · 1 filter

math.NT2023★ 1 cited

Probabilistic Galois Theory in Function Fields

Alexei Entin, Alexander Popov

We study the irreducibility and Galois group of random polynomials over function fields. We prove that a random polynomial $f = y^{n} + \sum_{i = 0}^{n - 1} a_{i} (x) y^{i} \in F_{q} [x] [y]$ wit…

math.NT2023

The Least Common Multiple of Polynomial Values over Function Fields

Alexei Entin, Sean Landsberg

Cilleruelo conjectured that for an irreducible polynomial $f \in Z [X]$ of degree $d \geq 2$ one has $$\log\left[\mathrm{lcm}(f(1),f(2),\ldots f(N))\right]\sim(d-1)N\log N$…

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}}+…