6 papers
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…
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…
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…
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…
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…
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 $\…