Congruences arising from Apéry-type series for zeta values

Recently, R. Tauraso established finite p-analogues of Apéryʼs famous 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 Zeilbergerʼs series for ζ(2) confirming a conjecture of Z.W. Sun.