Arithmetic properties of Apéry-like numbers

Eric Delaygue 1
1 CTN - Combinatoire, théorie des nombres
ICJ - Institut Camille Jordan [Villeurbanne]
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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  • HAL Id : hal-00873552, version 2
  • DOI : 10.1112

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Eric Delaygue. Arithmetic properties of Apéry-like numbers. Compositio Mathematica, Foundation Compositio Mathematica, 2018, 154 (2), ⟨10.1112⟩. ⟨hal-00873552v2⟩

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