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On Dwork's p-adic formal congruences theorem and hypergeometric mirror maps / E. Delaygue, T. Rivoal and J. Roques.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 246, no 1163.Publication details: Providence : American Mathematical Society, 2017.Description: v, 94 pages ; 26 cmISBN:
  • 9781470423001 (alk. paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
1. Introduction -- 2. Statements of the main results -- 3. Structure of the paper -- 4. Comments on the main results, comparison with previous results and open questions -- 5. The $p$-adic valuation of Pochhammer symbols -- 6. Proof of Theorem 4 -- 7. Formal congruences -- 8. Proof of Theorem 6 -- 9. Proof of Theorem 9 -- 10. Proof of Theorem 12 -- 11. Proof of Theorem 8 -- 12. Proof of Theorem 10 -- 13. Proof of Corollary 14 -- Bibliography.
Summary: Using Dwork's theory, the authors prove a broad generalization of his famous p-adic formal congruences theorem. This enables them 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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510 Am512 (Browse shelf(Opens below)) Available 138205
Total holds: 0

Includes bibliographical references.

1. Introduction --
2. Statements of the main results --
3. Structure of the paper --
4. Comments on the main results, comparison with previous results and open questions --
5. The $p$-adic valuation of Pochhammer symbols --
6. Proof of Theorem 4 --
7. Formal congruences --
8. Proof of Theorem 6 --
9. Proof of Theorem 9 --
10. Proof of Theorem 12 --
11. Proof of Theorem 8 --
12. Proof of Theorem 10 --
13. Proof of Corollary 14 --
Bibliography.

Using Dwork's theory, the authors prove a broad generalization of his famous p-adic formal congruences theorem. This enables them 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.

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