Arithmetic properties of Apéry-like numbers
arXiv:1310.4131 · doi:10.1112/S0010437X17007552
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.
25 pages. Version v2 contains cosmetic changes and a modification of the definition of -admissibility