Alexei Entin

activity

20162019

collaborators

4 papers

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

Factorization Statistics of Restricted Polynomial Specializations over Large Finite Fields

Alexei Entin

For a polynomial $F (t, A_{1}, \dots, A_{n}) \in F_{p} [t, A_{1}, \dots, A_{n}]$ ( $p$ being a prime number) we study the factorization statistics of its specializations $$F(t,a_1,\ldots,a_n…

math.NT2018

Monodromy of Hyperplane Sections of Curves and Decomposition Statistics over Finite Fields

Alexei Entin

For a projective curve $C \subset P^{n}$ defined over $F_{q}$ we study the statistics of the $F_{q}$ -structure of a section of $C$ by a random hyperplane defined…

math.NT2016

On square-free values of large polynomials over the rational function field

Dan Carmon, Alexei Entin

We investigate the density of square-free values of polynomials with large coefficients over the rational function field $F_{q} [t]$ . Some interesting questions answered as s…