Conference abstracts

Session S13 - Number Theory

July 25, 16:25 ~ 16:55

## The Mahler measure of elliptic curves

### Matilde Lalín

### Université de Montréal, Canada - mlalin@dms.umontreal.ca

The Mahler measure of a multivariable polynomial or rational function $P$ is given by the integral of $\log|P|$ where each of the variables moves on the unit circle and with respect to the Haar measure. In 1998 Boyd made a systematic numerical study of the Mahler measure of many polynomial families and found interesting conjectural relationships to special values of $L$-functions of elliptic curves. We will discuss some recent advances on Boyd's conjectures.