Congruences arising from Apéry-type series for zeta values

Abstract

Recently, R. Tauraso established finite $p$-analogues of famous Apéry series for $\zeta (2)$ and $\zeta (3).$ In this paper, we present several congruences for finite central binomial sums arising from the truncation of Apéry-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.

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

References in corpus (3)

• Super congruences and Euler numbers
• Congruences of alternating multiple harmonic sums
• A new series for ${\pi }^3$ and related congruences

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• More congruences from Apery-like formulae
• New properties of multiple harmonic sums modulo $p$ and $p$-analogues of Leshchiner's series
• From generating series to polynomial congruences