Comptes Rendus
no. 17-18
Number Theory
Analytic functions over Zp and p-regular sequences
[Fonctions analytiques sur Zp et suites p-régulières]

Présenté par : Jean-Pierre Kahane

Zhang Shu1 ; Jia-Yan Yao1
1 Department of Mathematics, Tsinghua University, 100084 Beijing, PR China
Comptes Rendus. Mathématique, Volume 349 (2011) no. 17-18, pp. 947-952.

Soit p un nombre premier. Dans ce travail, nous caractérisons les fonctions analytiques f:Zp→Cp sans zéros dans N pour lesquelles la suite (vp(f(n)))n≥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:Zp→Cp without roots in N for which the sequence (vp(f(n)))n≥0 is p-regular. Then we apply our characterization to study quadratic linear recurrent sequences.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.08.001
Zhang Shu 1 ; Jia-Yan Yao 1

1 Department of Mathematics, Tsinghua University, 100084 Beijing, PR China 
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Zhang Shu; Jia-Yan Yao. Analytic functions over $ {\mathbb{Z}}_{p}$ and p-regular sequences. Comptes Rendus. Mathématique, Volume 349 (2011) no. 17-18, pp. 947-952. doi : 10.1016/j.crma.2011.08.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.08.001/

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