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arXiv · 1310.4131

Arithmetic properties of Apéry-like numbers

Eric Delaygue
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Abstract

We provide lower bounds for p-adic valuations of multisums of factorial ratios which satisfy an Apéry-like recurrence relation: these include Apéry, Domb, Franel numbers, the numbers of abelian squares over a finite alphabet, and constant terms of powers of certain Laurent polynomials. In particular, we prove Beukers' conjectures on the p-adic valuation of Apéry numbers. Furthermore, we give an effective criterion for a sequence of factorial ratios to satisfy the p-Lucas property for almost all primes p.

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Eric Delaygue. 2015-11-18. Arithmetic properties of Apéry-like numbers. https://doi.org/10.1112/s0010437x17007552

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