Integral structures on p-adic fourier theory

Kenichi Bannai, Shinichi Kobayashi

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this article, we give an explicit construction of the p-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 K-locally analytic functions on the ring of integers OK for any finite extension K of Qp, generalizing the basis constructed by Amice for locally analytic functions on Zp. 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.

Original languageEnglish
Pages (from-to)521-550
Number of pages30
JournalAnnales de l'Institut Fourier
Volume66
Issue number2
Publication statusPublished - 2016

Fingerprint

P-adic
Analytic function
Bernoulli
Congruence
Fourier transform
Ring
Integer

Keywords

  • Amice transform
  • Bernoulli-Hurwitz number
  • Congruence
  • Integrality
  • Lubin-Tate group
  • P-adic distribution
  • P-adic Fourier theory
  • P-adic periods

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Integral structures on p-adic fourier theory. / Bannai, Kenichi; Kobayashi, Shinichi.

In: Annales de l'Institut Fourier, Vol. 66, No. 2, 2016, p. 521-550.

Research output: Contribution to journalArticle

Bannai, K & Kobayashi, S 2016, 'Integral structures on p-adic fourier theory', Annales de l'Institut Fourier, vol. 66, no. 2, pp. 521-550.
Bannai, Kenichi ; Kobayashi, Shinichi. / Integral structures on p-adic fourier theory. In: Annales de l'Institut Fourier. 2016 ; Vol. 66, No. 2. pp. 521-550.
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