Séminaire d'arithmétique à Lyon

The Mahler measure of exact polynomials in three variables

by Thu Ha Trieu


The Mahler measure of polynomials was introduced by Mahler in 1962. In 1980, Smyth discovered there is a link between the Mahler measure and some objects in Number theory, namely, Dirichlet L-functions and Riemann-Zeta functions. In the talk, we will first recall some fundamental results of Mahler measures. Then we will see how the Mahler measure of certain three-variable exact polynomials can express in terms of elliptic curve L-values and Dirichlet L-values, conditionally on Beilinson's conjecture. Finally, we will apply this method to obtain (under Beilinson's conjecture) some Mahler measure identities conjectured by D. Boyd and F. Brunault.