Congruences arising from Apéry-type series for zeta values

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

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