Arithmetic properties of Apéry-like numbers

Por • 20 oct, 2013 • Sección: Educacion

Eric Delaygue

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.

arXiv:1310.4131v1 [math.NT]

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