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

21 papers

math.PR2024

Moments of traces of random symplectic matrices and hyperelliptic $L$ -functions

Alexei Entin, Noam Pirani

We study matrix integrals of the form $\int_{USp (2n)} j = 1 \prod k tr (U^{j})^{a_{j}} d U,$ where $a_{1}, \dots, a_{r}$ are natural numbers and integration is with…

math.NT2024

Automorphism Groups of Finite Extensions of Fields and the Minimal Ramification Problem

Alexei Entin

We study the following question: given a global field $F$ and finite group $G$ , what is the minimal $r$ such that there exists a finite extension $K / F$ with $\mathrm{Aut}(K/F)\cong…

math.GR2024★ 1 cited

Normalizer Quotients of Symmetric Groups and Inner Holomorphs

Alexei Entin, Cindy Tsang

We show that every finite group $T$ is isomorphic to a normalizer quotient $N_{S_{n}} (H) / H$ for some $n$ and a subgroup $H \leq S_{n}$ . We show that this holds for all large enough $n\g…

math.AC2024

Maximal Ideals in Commutative Rings and the Axiom of Choice

Alexei Entin

It is well-known that within Zermelo-Fraenkel set theory (ZF), the Axiom of Choice (AC) implies the Maximal Ideal Theorem (MIT), namely that every nontrivial commutative ring has a…

math.NT2024

Galois groups of random polynomials over the rational function field

Alexei Entin

For a fixed prime power $q$ and natural number $d$ we consider a random polynomial $f = x^{n} + a_{n - 1} (t) x^{n - 1} + \dots + a_{1} (t) x + a_{0} (t) \in F_{q} [t] [x]$ with $a_{i}$ drawn uniformly…

math.NT2024

Lower Bounds on the Least Common Multiple of a Polynomial Sequence and its Radical

Alexei Entin

Cilleruelo conjectured that for an irreducible polynomial $f \in Z [X]$ of degree $d \geq 2$ , denoting $L_{f} (N) = lcm (f (1), f (2), \dots f (N))$ one has $$\log L_f(n)\…

Moments of traces of random symplectic matrices and hyperelliptic L-functions

Automorphism Groups of Finite Extensions of Fields and the Minimal Ramification Problem

Normalizer Quotients of Symmetric Groups and Inner Holomorphs

Maximal Ideals in Commutative Rings and the Axiom of Choice

Galois groups of random polynomials over the rational function field

Lower Bounds on the Least Common Multiple of a Polynomial Sequence and its Radical

Moments of traces of random symplectic matrices and hyperelliptic $L$ -functions