论文标题
3D Landau-Ginzburg潜力的Mahler度量
Mahler Measure of 3D Landau-Ginzburg Potentials
论文作者
论文摘要
我们以艾森斯坦 - 凯里克（Eisenstein-Kronecker）系列的方式表达了$ 23 $ laurent多项式家族的Mahler量度。这些劳伦（Laurent）多项式出现，因为Fano上的Landau-Ginzburg潜力$ 3 $ - FOLDS，其中$ 16 $定义了$ K3 $ K3 $ HYPERSURFACE的普通Picard等级$ 19 $，其余的Picard等级为$ <19 $。我们将每个理性的刻画模量的Mahler度量与$ 3 $ unction的$ 3 $的价值相关联，重量为$ 3 $ 3 $ newform。此外，我们发现这些家庭的Mahler措施中的$ 10 $异国关系。
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.
