# A Hypergeometric Version of the Modularity of Rigid Calabi-Yau Manifolds

```@article{Zudilin2018AHV,
title={A Hypergeometric Version of the Modularity of Rigid Calabi-Yau Manifolds},
author={W. Zudilin},
journal={Symmetry Integrability and Geometry-methods and Applications},
year={2018},
volume={14},
pages={086}
}```
• W. Zudilin
• Published 2018
• Mathematics, Physics
• Symmetry Integrability and Geometry-methods and Applications
• We examine instances of modularity of (rigid) Calabi-Yau manifolds whose periods are expressed in terms of hypergeometric functions. The \$p\$-th coefficients \$a(p)\$ of the corresponding modular form can be often read off, at least conjecturally, from the truncated partial sums of the underlying hypergeometric series modulo a power of \$p\$ and from Weil's general bounds \$|a(p)|\le2p^{(m-1)/2}\$, where \$m\$ is the weight of the form. Furthermore, the critical \$L\$-values of the modular form are… CONTINUE READING
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