Arithmetic properties of Apéry-like numbers
| Autor: | Eric Delaygue |
|---|---|
| Přispěvatelé: | Combinatoire, théorie des nombres (CTN), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Research supported by the project Holonomix (PEPS CNRS INS2I 2012), Delaygue, Eric |
| Rok vydání: | 2017 |
| Předmět: |
Factorial
Mathematics::Number Theory Constant terms of powers of Laurent polynomials p-Lucas property 0102 computer and information sciences Congruences 01 natural sciences Apéry's constant Combinatorics Apéry numbers 0101 mathematics Abelian group Mathematics Sequence Algebra and Number Theory Recurrence relation Mathematics - Number Theory 010102 general mathematics 2010 MSC: Primary 11B50 Secondary 11B65 05A10 Congruence relation 16. Peace & justice [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] 010201 computation theory & mathematics Physics::Accelerator Physics Alphabet Primary 11B50 Secondary 11B65 05A10 [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT] |
| Zdroj: | Compositio Mathematica Compositio Mathematica, Foundation Compositio Mathematica, 2018, 154 (2) |
| ISSN: | 1570-5846 0010-437X |
| DOI: | 10.1112/s0010437x17007552 |
| Popis: | 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. Comment: 25 pages. Version v2 contains cosmetic changes and a modification of the definition of $r$-admissibility |
| Databáze: | OpenAIRE |
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