English

Supercongruences for a truncated hypergeometric series

Number Theory 2011-05-24 v2 Combinatorics

Abstract

The purpose of this note is to obtain some congruences modulo a power of a prime pp involving the truncated hypergeometric series k=1p1(x)k(1x)k(1)k21ka\sum_{k=1}^{p-1} {(x)_k(1-x)_k\over (1)_k^2}\cdot{1\over k^a} for a=1a=1 and a=2a=2. In the last section, the special case x=1/2x=1/2 is considered.

Keywords

Cite

@article{arxiv.1007.3852,
  title  = {Supercongruences for a truncated hypergeometric series},
  author = {Roberto Tauraso},
  journal= {arXiv preprint arXiv:1007.3852},
  year   = {2011}
}

Comments

Revised version

R2 v1 2026-06-21T15:51:26.453Z