In this article, we give an explicit construction of the -adic Fourier transform by Schneider and Teitelbaum, which allows for the investigation of the integral property. As an application, we give a certain integral basis of the space of -locally analytic functions on the ring of integers for any finite extension of , generalizing the basis constructed by Amice for locally analytic functions on . We also use our result to prove congruences of Bernoulli-Hurwitz numbers at non-ordinary (i.e. supersingular) primes originally investigated by Katz and Chellali.
Dans cet article, nous donnons une construction explicite de la transformation de Fourier -adique de Schneider et Teitelbaum, qui nous permet d’étudier son integralité. Comme application, pour toute extension finie de nous donnons une certaine base entière de l’espace de -fonctions localement analytiques sur l’anneau des entiers , en généralisant la base construite par Amice pour les fonctions localement analytiques sur . Nous utilisons également notre résultat pour démontrer certaines relations de congruence étudiées initialement par Katz et Chellali entre nombres de Bernoulli-Hurwitz aux places non-ordinaires (c’est-à-dire supersingulières).
Accepted:
Published online:
Classification: 11S40
Keywords: -adic distribution, -adic Fourier theory, Amice transform, integrality, congruence, Lubin-Tate group, Bernoulli-Hurwitz number, -adic periods
@article{AIF_2016__66_2_521_0, author = {Bannai, Kenichi and Kobayashi, Shinichi}, title = {Integral structures on $p$-adic {Fourier} theory}, journal = {Annales de l'Institut Fourier}, pages = {521--550}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {66}, number = {2}, year = {2016}, doi = {10.5802/aif.3018}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3018/} }
TY - JOUR TI - Integral structures on $p$-adic Fourier theory JO - Annales de l'Institut Fourier PY - 2016 DA - 2016/// SP - 521 EP - 550 VL - 66 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3018/ UR - https://doi.org/10.5802/aif.3018 DO - 10.5802/aif.3018 LA - en ID - AIF_2016__66_2_521_0 ER -
Bannai, Kenichi; Kobayashi, Shinichi. Integral structures on $p$-adic Fourier theory. Annales de l'Institut Fourier, Volume 66 (2016) no. 2, pp. 521-550. doi : 10.5802/aif.3018. https://aif.centre-mersenne.org/articles/10.5802/aif.3018/
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