Linear Mahler Measures and Double L-values of Modular Forms

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.

Final version. Accepted to the Journal of Number Theory

References in corpus (1)

• Transformations of $L$-values

Cited by in corpus (2)

• A Proof of the Conjecture of Lehmer and of the Conjecture of Schinzel-Zassenhaus
• Apéry's theorem and problems for the values of Riemann's zeta function and their $q$-analogues