English

Some supercongruences on truncated ${}_3F_2$ hypergeometric series

Number Theory 2018-02-13 v3 Combinatorics

Abstract

In 2003, Rodriguez-Villegas conjectured four supercongruences on the truncated 3F2{}_3F_2 hypergeometric series for certain modular K3 surfaces, which were gradually proved by several authors. Motivated by some supercongruences on combinatorial numbers such as Ap\'ery numbers and Domb numbers, we establish some new supercongruences on the truncated 3F2{}_3F_2 hypergeometric series, which extend the four Rodriguez-Villegas supercongruences.

Keywords

Cite

@article{arxiv.1610.03799,
  title  = {Some supercongruences on truncated ${}_3F_2$ hypergeometric series},
  author = {Ji-Cai Liu},
  journal= {arXiv preprint arXiv:1610.03799},
  year   = {2018}
}

Comments

to appear in J. Difference Equ. Appl., 14 pages

R2 v1 2026-06-22T16:18:59.617Z