### 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 language | English |
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Pages (from-to) | 521-550 |

Number of pages | 30 |

Journal | Annales de l'Institut Fourier |

Volume | 66 |

Issue number | 2 |

Publication status | Published - 2016 |

### 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

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## Cite this

Bannai, K., & Kobayashi, S. (2016). Integral structures on p-adic fourier theory.

*Annales de l'Institut Fourier*,*66*(2), 521-550.