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arXiv · 1206.1454

Linear Mahler Measures and Double L-values of Modular Forms

Evgeny Shinder·Masha Vlasenko
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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.

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Evgeny Shinder, Masha Vlasenko. 2014-02-13. Linear Mahler Measures and Double L-values of Modular Forms. https://arxiv.org/abs/1206.1454

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