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arXiv · 2308.10813

On $L$-derivatives and biextensions of Calabi-Yau motives

V. Golyshev
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Abstract

We prove that certain differential operators of the form $DLD$ with $L$ hypergeometric and $D=z \frac{d}{dz}$ are of Picard-Fuchs type. We give closed hypergeometric expressions for minors of the biextension period matrices that arise from certain rank 4 weight 3 Calabi-Yau motives presumed to be of analytic rank 1. We compare their values numerically to the first derivative of the $L$-functions of the respective motives at $s=2$.

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V. Golyshev. 2023-08-21. On $L$-derivatives and biextensions of Calabi-Yau motives. https://arxiv.org/abs/2308.10813

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