Mahler measure of successively exact polynomials

Abstract: The relation between Mahler measures of polynomials and special values of L-functions has been widely explored since the seminal works of Boyd, Deninger and Rodriguez-Villegas in the late '90s. Sometimes, as in the earliest examples computed by Smyth, these relations occur between Mahler measures of n-variable polynomials and special values associated to geometric objects of dimension strictly less than n-1. This phenomenon has found a first explanation in the notion of exactness, put forward by Maillot and Lalín. In this talk, based on joint work in progress with François Brunault, we will give a survey of these questions, and explain how one can interpret them using new cohomological approaches, which provide a notion of successive exactness, predicted by Lalín, that explains the observed drops in the dimension of the geometric objects used to construct the L-functions whose special values should be related to the Mahler measure of the polynomial in question.

number theory

Audience: researchers in the topic

Japan Europe Number Theory Exchange Seminar

Series comments: The purpose of the Japan Europe Number Theory Exchange Seminar is to give a opportunity for researchers in Japan and Europe to exchange their research projects by giving short talks (30 min). The target audience are researchers of any level in the area of number theory.

Start for Fall 2021: 26th October