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Binomial Coefficient - Harmonic Sum Identities Associated to Supercongruences.
- Source :
-
Integers . Dec2011, Vol. 11 Issue 6, p801-809. 9p. - Publication Year :
- 2011
-
Abstract
- We establish two binomial coefficient-generalized harmonic sum identities using the partial fraction decomposition method. These identities are a key ingredient in the proofs of numerous supercongruences. In particular, in other works of the author, they are used to establish modulo pk ( k > 1) congruences between truncated generalized hypergeometric series, and a function which extends Greene's hypergeometric function over finite fields to the p-adic setting. A specialization of one of these congruences is used to prove an outstanding conjecture of Rodriguez-Villegas which relates a truncated generalized hypergeometric series to the p-th Fourier coefficient of a particular modular form. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 18670652
- Volume :
- 11
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Integers
- Publication Type :
- Academic Journal
- Accession number :
- 67517162
- Full Text :
- https://doi.org/10.1515/INTEG.2011.061