Mahler measures of polynomials have been known to be periods of Deligne cohomology since the seminal work of Deninger. This explains some links between Mahler measures and special values of L-functions, which were observed by Boyd and Rodriguez-Villegas, and proven in some cases using the method of Rogers and Zudilin, which allows one to perform explicit regulator computations using Eisenstein series. In this talk, based on a joint work in progress with François Brunault, I will outline a general construction which exhibits the Mahler measure as a mixed period, and allows to explain motivically more relations between Mahler measures and special values of L-functions. If time permits, we will briefly talk about possible generalizations of the Rogers-Zudilin method to this setting.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/11596