Lucas congruences for the Apéry numbers modulo p²

Yassawi, Reem; Rowland, Eric and Krattenthaler, Christian (2021). Lucas congruences for the Apéry numbers modulo p². Integers, 21, article no. A20.

URL: http://math.colgate.edu/~integers/v20/v20.pdf

Abstract

The sequence A(n)n≥0 of Apéry numbers can be interpolated to the complex numbers by an entire function. We give a formula for the Taylor coefficients of this function, centered at the origin, as a Z-linear combination of multiple zeta values. We then show that for integers n whose base-p digits belong to a certain set, A(n) satisfies a Lucas congruence modulo prime squares.

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