Analytic functions over $ {\mathbb{Z}}_{p}$ and <i>p</i>-regular sequences

Shu, Zhang; Yao, Jia-Yan

doi:10.1016/j.crma.2011.08.001

Number Theory

Analytic functions over

Z_{p}

and p-regular sequences
[Fonctions analytiques sur

Z_{p}

et suites p-régulières]

Présenté par : Jean-Pierre Kahane

Shu, Zhang ¹ ; Yao, Jia-Yan ¹

¹ Department of Mathematics, Tsinghua University, 100084 Beijing, PR China

Comptes Rendus. Mathématique, Tome 349 (2011) no. 17-18, pp. 947-952.

Résumé
Abstract

Soit p un nombre premier. Dans ce travail, nous caractérisons les fonctions analytiques $f : Z_{p} \to C_{p}$ sans zéros dans $N$ pour lesquelles la suite $(v_{p} (f {(n)))}_{n \geq 0}$ est p-régulière. Ensuite nous appliquons notre caractérisation pour étudier les suites récurrentes linéaires quadratiques.

Let p be a prime number. In this work we characterize all the analytic functions $f : Z_{p} \to C_{p}$ without roots in $N$ for which the sequence $(v_{p} (f {(n)))}_{n \geq 0}$ is p-regular. Then we apply our characterization to study quadratic linear recurrent sequences.

Reçu le : 2011-06-13
Accepté le : 2011-08-01
Publié le : 2011-08-31

DOI : 10.1016/j.crma.2011.08.001

Affiliations des auteurs :

Shu, Zhang ¹ ; Yao, Jia-Yan ¹

¹ Department of Mathematics, Tsinghua University, 100084 Beijing, PR China

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     title = {Analytic functions over $ {\mathbb{Z}}_{p}$ and \protect\emph{p}-regular sequences},
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     pages = {947--952},
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Shu, Zhang; Yao, Jia-Yan. Analytic functions over $ {\mathbb{Z}}_{p}$ and p-regular sequences. Comptes Rendus. Mathématique, Tome 349 (2011) no. 17-18, pp. 947-952. doi : 10.1016/j.crma.2011.08.001. http://www.numdam.org/articles/10.1016/j.crma.2011.08.001/

Bibliographie
Cité par

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[6] Medina, L.A.; Rowland, E.S. p-regularity of the p-adic valuation of the Fibonacci sequence | arXiv

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