Congruences arising from Ap\'ery-type series for zeta values

Khodabakhsh Hessami Pilehrood; Tatiana Hessami Pilehrood

doi:10.1016/j.aam.2012.05.003

Congruences arising from Ap\'ery-type series for zeta values

Number Theory 2013-12-31 v3 Combinatorics

Authors: Khodabakhsh Hessami Pilehrood , Tatiana Hessami Pilehrood

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Abstract

Recently, R. Tauraso established finite $p$ -analogues of famous Ap\'ery series for $\zeta(2)$ and $\zeta(3).$ In this paper, we present several congruences for finite central binomial sums arising from the truncation of Ap\'ery-type series for $\zeta(4)$ and $\zeta(5).$ We also prove a $p$ -analogue of Zeilberger's series for $\zeta(2)$ confirming a conjecture of Z. W. Sun.

Keywords

congruences Apéry-type series zeta values p-analogues central binomial sums Zeilberger series

Cite

@article{arxiv.1108.1893,
  title  = {Congruences arising from Ap\'ery-type series for zeta values},
  author = {Khodabakhsh Hessami Pilehrood and Tatiana Hessami Pilehrood},
  journal= {arXiv preprint arXiv:1108.1893},
  year   = {2013}
}

Comments

19 pages; to appear in Adv. in Appl. Math

Congruences arising from Ap\'ery-type series for zeta values

Abstract

Keywords

Cite

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