A Hypergeometric Version of the Modularity of Rigid Calabi-Yau Manifolds
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 often be read off, at least conjecturally, from the truncated partial sums of the underlying hypergeom...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209764 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | A Hypergeometric Version of the Modularity of Rigid Calabi-Yau Manifolds / W. Zudilin // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 37 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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 often be 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.
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| ISSN: | 1815-0659 |