Fonctions $L$ $ $p$-adiques et irrationalité

Bel, Pierre

Fonctions

L

p

-adiques et irrationalité

Bel, Pierre ¹

¹ Institut de Mathématiques de Bordeaux, UMR 5251, Université Bordeaux 1, 351, cours de la Libération, 33405 Talence cedex, France

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 1, pp. 189-227.

Résumé

We give a minoration of the dimension of the vector space spanned on a cyclotomic field by the values of $p$ -adic Hurwitz zeta function. As a corollary, we obtain the existence of irrationality values of $p$ -adic $L$ functions. The proof uses hypergeometric series and a criterion of linear independence.

MR Zbl | 1 citation dans Numdam

Classification : 11J72, 11J61

Affiliations des auteurs :

Bel, Pierre ¹

¹ Institut de Mathématiques de Bordeaux, UMR 5251, Université Bordeaux 1, 351, cours de la Libération, 33405 Talence cedex, France

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     title = {Fonctions $L$ $ $p$-adiques et irrationalit\'e},
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     pages = {189--227},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 9},
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Bel, Pierre. Fonctions $L$ $ $p$-adiques et irrationalité. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 1, pp. 189-227. http://archive.numdam.org/item/ASNSP_2010_5_9_1_189_0/

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