Mahler Measure of 3D Landau-Ginzburg Potentials

Jiarui Fei

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arXiv · 2009.09701

Mahler Measure of 3D Landau-Ginzburg Potentials

Jiarui Fei

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Abstract

We express the Mahler measures of $23$ families of Laurent polynomials in terms of Eisenstein-Kronecker series. These Laurent polynomials arise as Landau-Ginzburg potentials on Fano $3$-folds, $16$ of which define $K3$ hypersurfaces of generic Picard rank $19$, and the rest are of generic Picard rank $< 19$. We relate the Mahler measure at each rational singular moduli to the value at $3$ of the $L$-function of some weight-$3$ newform. Moreover, we find $10$ exotic relations among the Mahler measures of these families.

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Jiarui Fei. 2020-09-21. Mahler Measure of 3D Landau-Ginzburg Potentials. https://arxiv.org/abs/2009.09701

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