We give a minoration of the dimension of the vector space spanned on a cyclotomic field by the values of -adic Hurwitz zeta function. As a corollary, we obtain the existence of irrationality values of -adic functions. The proof uses hypergeometric series and a criterion of linear independence.
@article{ASNSP_2010_5_9_1_189_0, author = {Bel, Pierre}, title = {Fonctions $L$ $ $p$-adiques et irrationalit\'e}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {189--227}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 9}, number = {1}, year = {2010}, mrnumber = {2668878}, zbl = {1203.11051}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2010_5_9_1_189_0/} }
TY - JOUR AU - Bel, Pierre TI - Fonctions $L$ $ $p$-adiques et irrationalité JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2010 SP - 189 EP - 227 VL - 9 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2010_5_9_1_189_0/ LA - en ID - ASNSP_2010_5_9_1_189_0 ER -
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://www.numdam.org/item/ASNSP_2010_5_9_1_189_0/
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