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

Title: A Hypergeometric Version of the Modularity of Rigid Calabi-Yau Manifolds
Creator: Zudilin, Wadim
Relation: Symmetry, Integrability and Geometry: Methods and Applications Vol. 14, no. 086
Publisher Link: http://dx.doi.org/10.3842/SIGMA.2018.086
Publisher: National Academy of Sciences of Ukraine, Institute of Mathematics
Resource Type: journal article
Date: 2018
Description: 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)|≤2p(m−1)/2, where m is the weight of the form. Furthermore, the critical L-values of the modular form are predicted to be Q-proportional to the values of a related basis of solutions to the hypergeometric differential equation.
Subject: hypergeometric equation; bilateral hypergeometric series; modular form; Calabi-Yau manifold
Identifier: http://hdl.handle.net/1959.13/1446364
Identifier: uon:42845
Identifier: ISSN:1815-0659
Language: eng
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