We give a sufficient condition on a rational to get the irrationality of . In particular, for a prime , the number is irrational. If this condition is satisfied, we give a bound for the irrationality measure of .
Nous donnons un condition suffisante sur un rationnel pour que le nombre soit irrationnel. En particulier, pour tout nombre premier , le nombre est irrationnel. Si cette condition est remplie, nous donnons de plus une borne pour la mesure d’irrationalité de .
Accepted:
Published online:
DOI: 10.5802/jtnb.1069
Classification: 11J72, 11J82, 11M35
Keywords: Irrationality, -adic Hurwitz zeta function, measure
Author's affiliations:
@article{JTNB_2019__31_1_81_0, author = {Pierre Bel}, title = {Irrationalit\'e des valeurs de $\zeta _p(4, x)$}, journal = {Journal de Th\'eorie des Nombres de Bordeaux}, pages = {81--99}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {31}, number = {1}, year = {2019}, doi = {10.5802/jtnb.1069}, mrnumber = {3994720}, language = {fr}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1069/} }
TY - JOUR TI - Irrationalité des valeurs de $\zeta _p(4, x)$ JO - Journal de Théorie des Nombres de Bordeaux PY - 2019 DA - 2019/// SP - 81 EP - 99 VL - 31 IS - 1 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1069/ UR - https://www.ams.org/mathscinet-getitem?mr=3994720 UR - https://doi.org/10.5802/jtnb.1069 DO - 10.5802/jtnb.1069 LA - fr ID - JTNB_2019__31_1_81_0 ER -
Pierre Bel. Irrationalité des valeurs de $\zeta _p(4, x)$. Journal de Théorie des Nombres de Bordeaux, Volume 31 (2019) no. 1, pp. 81-99. doi : 10.5802/jtnb.1069. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1069/
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