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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