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arXiv · 2005.04801

Lucas congruences for the Ap\'ery numbers modulo $p^2$

Eric Rowland·Reem Yassawi·Christian Krattenthaler
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Abstract

The sequence $A(n)_{n \geq 0}$ of Ap\'ery 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 $p^2$.

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Eric Rowland, Reem Yassawi, Christian Krattenthaler. 2020-05-10. Lucas congruences for the Ap\'ery numbers modulo $p^2$. https://arxiv.org/abs/2005.04801

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