English

Supercongruences for truncated hypergeometric series and p-adic gamma function

Number Theory 2018-07-11 v5

Abstract

We prove three more general supercongruences between truncated hypergeometric series and pp-adic Gamma function from which some known supercongruences follow. A supercongruence conjectured by Rodriguez-Villegas and proved by E. Mortenson using the theory of finite field hypergeometric series follows from one of our more general supercongruences. We also prove a supercongruence for 7F6{_7}F_6 truncated hypergeometric series which is similar to a supercongruence proved by L. Long and R. Ramakrishna.

Keywords

Cite

@article{arxiv.1507.07391,
  title  = {Supercongruences for truncated hypergeometric series and p-adic gamma function},
  author = {Rupam Barman and Neelam Saikia},
  journal= {arXiv preprint arXiv:1507.07391},
  year   = {2018}
}

Comments

To appear in Mathematical Proceedings Cambridge Phil. Soc

R2 v1 2026-06-22T10:19:23.732Z