Mahler measure of a family of exact polynomials

Abstract: I will present results around the Mahler measure of a family of 2-variate exact polynomials. The closed formula for the Mahler measure of two-variable exact polynomials gives an expression of each of these Mahler measures as a finite sum of the values of Dilogarithm at certain roots of unity.

This allows to compute their values with any precision, and to use the techniques of Riemann sums to compute the limit of this sequence of Mahler measures and an asymptotic expansion, with a link to a theorem of Boyd and Lawton. Finally, for small values of d, we can relate these Mahler measures to values of special values of L-function, with a link with works of Boyd-Rodriguez Villegas and others.

algebraic geometrynumber theory

Audience: researchers in the topic

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Rendez-vous on special values and periods

Series comments: The main objective of this conference is to gather together young researchers interested in special values of L-functions and periods. These objects are at the crossroads of many recent important developments in arithmetic geometry, such as Euler systems or the theory of motives. The different talks will portray the variety of viewpoints with which L-functions and periods are studied at present.

Registration is free and mandatory, to get access to the livestream and recording of the talks.

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