Mathematics – Number Theory
Scientific paper
2012-04-06
Integers 11 (2011), A37, 8 pp
Mathematics
Number Theory
Scientific paper
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 $p^k$ ($k>1$) 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.
No associations
LandOfFree
Binomial coefficient-harmonic sum identities associated to supercongruences does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Binomial coefficient-harmonic sum identities associated to supercongruences, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Binomial coefficient-harmonic sum identities associated to supercongruences will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-36930