| Description |
1 online resource (v, 94 pages) |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 246, number 1163 |
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Memoirs of the American Mathematical Society ; no. 1163.
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| Contents |
Chapter 1. Introduction Chapter 2. Statements of the main results Chapter 3. Structure of the paper Chapter 4. Comments on the main results, comparison with previous results and open questions Chapter 5. The $p$-adic valuation of Pochhammer symbols Chapter 6. Proof of Theorem 4 Chapter 7. Formal congruences Chapter 8. Proof of Theorem 6 Chapter 9. Proof of Theorem 9 Chapter 10. Proof of Theorem 12 Chapter 11. Proof of Theorem 8 Chapter 12. Proof of Theorem 10 Chapter 13. Proof of Corollary 14 |
| Summary |
"Using Dwork's theory, we prove a broad generalization of his famous -adic formal congruences theorem. This enables us to prove certain p-adic congruences for the generalized hypergeometric series with rational parameters; in particular, they hold for any prime number p and not only for almost all primes. Furthermore, using Christol's functions, we provide an explicit formula for the "Eisenstein constant" of any hypergeometric series with rational parameters. As an application of these results, we obtain an arithmetic statement "on average" of a new type concerning the integrality of Taylor coefficients of the associated mirror maps. It contains all the similar univariate integrality results in the literature, with the exception of certain refinements that hold only in very particular cases."--Publisher website |
| Notes |
"Volume 246, Number 1163 (second of 6 numbers), March 2017." |
| Bibliography |
Includes bibliographical references (pages 93-94) |
| Notes |
Print version record |
| Subject |
Geometry, Algebraic.
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p-adic analysis.
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Congruences (Geometry)
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Mirror symmetry.
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MATHEMATICS -- Algebra -- Intermediate.
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Congruences (Geometry)
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Geometry, Algebraic
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Mirror symmetry
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p-adic analysis
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| Form |
Electronic book
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| Author |
Rivoal, T. (Tanguy), 1972- author.
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Roques, J. (Julien), 1980- author.
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American Mathematical Society, publisher
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| ISBN |
9781470436353 |
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1470436353 |
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