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arXiv · 2510.23298

Galois Groups of Ap\'ery-like Series Modulo Primes

Xavier Caruso·Florian Fürnsinn·Daniel Vargas-Montoya·Wadim Zudilin
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Abstract

We compute the Galois groups of the reductions modulo the prime numbers $p$ of the generating series of Ap\'ery numbers, Domb numbers and Almkvist--Zudilin numbers. We observe in particular that their behavior is governed by congruence conditions on p.

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Xavier Caruso, Florian Fürnsinn, Daniel Vargas-Montoya, Wadim Zudilin. 2025-10-27. Galois Groups of Ap\'ery-like Series Modulo Primes. https://doi.org/10.1017/s0004972725100932

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