Integral structures on $p$-adic Fourier theory

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 ${\mathcal{O}}_K$ for any finite extension $K$ of ${\mathbb{Q}}_p$, generalizing the basis constructed by Amice for locally analytic functions on ${\mathbb{Z}}_p$. 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.

26 pages. v3. rewrote the introduction. Minor corrections

References in corpus (2)

• Algebraic theta functions and p-adic interpolation of Eisenstein-Kronecker numbers
• Algebraic theta functions and Eisenstein-Kronecker numbers