Various theorems in elementary -adic analysis, commonly proved only for and summarized in [4], are generalized to any local field, using the concept of a Mahler basis. In the last section we explain the relation of these results to the work [10]. The paper is largely self-contained.
Divers théorèmes d’analyse -adique élémentaires, souvent prouvés uniquement sur (cf. [4]), sont généralisés à tout corps local, avec l’aide de la notion de base de Mahler. Dans la dernière section nous expliquons la relation entre nos résultats et ceux de [10].
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Accepted:
Published online:
DOI: 10.5802/jtnb.955
Keywords: Mahler’s theorem, Amice transform, locally analytic distributions, Lubin-Tate groups
@article{JTNB_2016__28_3_597_0,
author = {Ehud de Shalit},
title = {Mahler bases and elementary $p$-adic analysis},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {597--620},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {28},
number = {3},
year = {2016},
doi = {10.5802/jtnb.955},
zbl = {1409.11113},
mrnumber = {3610689},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.955/}
}
TY - JOUR AU - Ehud de Shalit TI - Mahler bases and elementary $p$-adic analysis JO - Journal de théorie des nombres de Bordeaux PY - 2016 SP - 597 EP - 620 VL - 28 IS - 3 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.955/ DO - 10.5802/jtnb.955 LA - en ID - JTNB_2016__28_3_597_0 ER -
%0 Journal Article %A Ehud de Shalit %T Mahler bases and elementary $p$-adic analysis %J Journal de théorie des nombres de Bordeaux %D 2016 %P 597-620 %V 28 %N 3 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.955/ %R 10.5802/jtnb.955 %G en %F JTNB_2016__28_3_597_0
Ehud de Shalit. Mahler bases and elementary $p$-adic analysis. Journal de théorie des nombres de Bordeaux, Volume 28 (2016) no. 3, pp. 597-620. doi : 10.5802/jtnb.955. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.955/
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