Some progress regarding Chinburg’s conjecture in Mahler measure theory

by Mahya Mehrabdollahei

Friday 24 May 2024, 13:15 → 14:15 Europe/Zurich

HS5 (MI)

Mahler measure is a type of height function for univariate and multivariate polynomials P, defined as the arithmetic mean of log |P| over the torus. The study of sequences of Mahler measures was first started by Boyd and Lawton to address Lehmer’s Conjecture. Though the conjecture remains open, the strategy of studying the Mahler measure of sequences of multivariate polynomials has led to significant theorems in the field. In this talk, we will see how this strategy is fruitful for finding partial solutions to a conjecture by T. Chinburg. The conjecture is about a link between the Mahler measure of multivariate polynomials and special values of Dirichlet L-functions. All the prerequisites will be defined and discussed during the talk.