Linear Mahler Measures and Double L-values of Modular Forms
Number Theory
2016-09-20 v4
Abstract
We consider the Mahler measure of the polynomial 1+x_1+x_2+x_3+x_4, which is the first case not yet evaluated explicitly. A conjecture due to F. Rodriguez-Villegas represents this Mahler measure as a special value at the point 4 of the L-function of a modular modular form of weight 3. We prove that this Mahler measure is equal to a linear combination of double L-values of certain meromorphic modular forms of weight 4.
Keywords
Cite
@article{arxiv.1206.1454,
title = {Linear Mahler Measures and Double L-values of Modular Forms},
author = {Evgeny Shinder and Masha Vlasenko},
journal= {arXiv preprint arXiv:1206.1454},
year = {2016}
}
Comments
Final version. Accepted to the Journal of Number Theory