activity
20242026
collaborators

6 papers

math.NT2026

The strong form of Van der Waerden's conjecture via twisted Chowla

Theresa C. Anderson, Sam Chow, Rainer Dietmann +3

Determining the properties of a random polynomial has fuelled significant investigation over the past century. One driving force of this research is a 1936 paper of Van der Waerden…

math.NT2026

The asymptotic Mahler measure of Gaussian periods

Gunther Cornelissen, David Hokken, Berend Ringeling

We construct a sequence of cyclotomic integers (Gaussian periods) of particularly small Mahler measure/height. We study the asymptotics of their Mahler measure as a function of the…

math.NT2026

Relating Mahler measures and Dirichlet -values: new evidence for Chinburg's conjectures

David Hokken, Mahya Mehrabdollahei, Berend Ringeling

Let be the odd quadratic Dirichlet character of conductor , and let denote the Mahler measure of a polynomial . In 1984, Chinburg conjectured that f…

math.NT2025

Irreducibility and Galois groups of random reciprocal polynomials of large degree

David Hokken, Dimitris Koukoulopoulos

Let be a monic reciprocal polynomial of degree sampled randomly by selecting its coefficient…

math.NT2025

Counting (skew-)reciprocal Littlewood polynomials with square discriminant

David Hokken

A Littlewood polynomial is a single-variable polynomial all of whose coefficients lie in . We establish the leading term asymptotics of the number of reciprocal or skew…

math.DS2024

Topology of zero sets of polynomials with square discriminant

David Hokken

Let be a fixed set of integers, closed under multiplication, closed under negation, or containing . We prove that any zero of a polynomial in $\…