Séminaire d'arithmétique à Lyon

Mahler measure and elliptic curves with complex multiplications

by Riccardo Pengo (Université de Copenhague)

Salle M7 (UMPA, ENS de Lyon)

Salle M7

UMPA, ENS de Lyon


Elliptic curves with complex multiplication have historically formed a fertile test ground for many conjectures on the arithmetic of elliptic curves. In this talk, we will explore one instance of this phenomenon by looking at the conjectures relating special values of L-functions to the Mahler measure of polynomials in multiple variables. These conjectures, initiated by the work of Boyd on Lehmer’s problem, can be approached for elliptic curves with complex multiplication using the proof of the Beilinson conjectures for CM elliptic curves, due to Deninger and Rohrlich.