### 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 |
---|---|

Pages (from-to) | 521-550 |

Number of pages | 30 |

Journal | Annales de l'Institut Fourier |

Volume | 66 |

Issue number | 2 |

Publication status | Published - 2016 |

### Fingerprint

### 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

*Annales de l'Institut Fourier*,

*66*(2), 521-550.

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

Research output: Contribution to journal › Article

*Annales de l'Institut Fourier*, vol. 66, no. 2, pp. 521-550.

}

TY - JOUR

T1 - Integral structures on p-adic fourier theory

AU - Bannai, Kenichi

AU - Kobayashi, Shinichi

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Amice transform

KW - Bernoulli-Hurwitz number

KW - Congruence

KW - Integrality

KW - Lubin-Tate group

KW - P-adic distribution

KW - P-adic Fourier theory

KW - P-adic periods

UR - http://www.scopus.com/inward/record.url?scp=84960905273&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84960905273&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84960905273

VL - 66

SP - 521

EP - 550

JO - Annales de l'Institut Fourier

JF - Annales de l'Institut Fourier

SN - 0373-0956

IS - 2

ER -