Mahler measures of algebraic varieties: Results and experiments

Abstract: The (logarithmic) Mahler measures of an $n$-variable polynomial $P$ is defined as the arithmetic mean of $\log |P|$ over the $n$-torus. Despite its purely analytic formulation, Mahler measure is known to have a deep connection with the arithmetic of the corresponding algebraic variety via $L$-functions, thanks to work of Deninger, Boyd, Bertin, and many others. There are several known results and conjectures in the literature relating Mahler measures to special $L$-values of Dirichlet series, elliptic curves, $K3$ surfaces, and modular forms. In this talk, we will give a survey of recent results in this research direction from both theoretical and experimental perspectives.

number theoryrepresentation theory

Audience: researchers in the topic

Comments: zoom: 658 593 56935, password: the first 6 digits of $\zeta(3)$

SJTU number theory seminar