Arithmetic properties of Ap\'ery-like numbers
Number Theory
2019-02-20 v2
Abstract
We provide lower bounds for p-adic valuations of multisums of factorial ratios which satisfy an Ap\'ery-like recurrence relation: these include Ap\'ery, 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 Ap\'ery numbers. Furthermore, we give an effective criterion for a sequence of factorial ratios to satisfy the p-Lucas property for almost all primes p.
Cite
@article{arxiv.1310.4131,
title = {Arithmetic properties of Ap\'ery-like numbers},
author = {Eric Delaygue},
journal= {arXiv preprint arXiv:1310.4131},
year = {2019}
}
Comments
25 pages. Version v2 contains cosmetic changes and a modification of the definition of $r$-admissibility