Alexei Entin

collaborators

4 papers

math.NT2025

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)\…

math.AC2025

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.NT2025

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.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…