[Les logarithmes plus et moins et la transformation d'Amice]
Nous donnons une nouvelle description des logarithmes p-adiques plus et moins définis par Pollack en termes de distributions. En particulier, si dénote la pré-image de sous la transformation d'Amice, nous donnons des formules explicites pour les valeurs pour tout et tout entier . Nos formules impliquent que la distribution correspond à une distribution étudiée par Koblitz en 1977. Par ailleurs, nous montrons qu'il existe une description similaire, due à Loeffler, pour des analogues à deux variables de ces logarithmes plus et moins.
We give a new description of Pollack's plus and minus p-adic logarithms in terms of distributions. In particular, if denote the pre-images of under the Amice transform, we give explicit formulae for the values for all and all integers . Our formulae imply that the distribution agrees with a distribution studied by Koblitz in 1977. Furthermore, we show that a similar description exists for Loeffler's two-variable analogues of these plus and minus logarithms.
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@article{CRMATH_2017__355_9_942_0,
author = {C\'edric Dion and Antonio Lei},
title = {Plus and minus logarithms and {Amice} transform},
journal = {Comptes Rendus. Math\'ematique},
pages = {942--948},
publisher = {Elsevier},
volume = {355},
number = {9},
year = {2017},
doi = {10.1016/j.crma.2017.09.012},
language = {en},
}
Cédric Dion; Antonio Lei. Plus and minus logarithms and Amice transform. Comptes Rendus. Mathématique, Volume 355 (2017) no. 9, pp. 942-948. doi : 10.1016/j.crma.2017.09.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.09.012/
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