Lucas congruences for the Apéry numbers modulo $p^2$

Abstract

The sequence $A(n{)}_{n\ge 0}$ of Apéry numbers can be interpolated to $\mathbb{C}$ by an entire function. We give a formula for the Taylor coefficients of this function, centered at the origin, as a $\mathbb{Z}$-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 $p^2$.

13 pages, 1 figure; publication version

References in corpus (1)

• Interpolated sequences and critical $L$-values of modular forms