Congruences arising from Apéry-type series for zeta values

Details Congruences arising from Apéry-type series for zeta values Congruences arising from Apéry-type series for zeta values

2011-08-09

arxiv.org/abs/1108.1893v2

Mathematics

Number Theory

19 pages

Scientific paper

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.

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