Note on $p$-adic Local Functional Equation
Number Theory
2022-06-23 v2 Algebraic Geometry
Abstract
Given primes , we record here a -adic valued Fourier theory on a local field over , which is developed under the perspective of group schemes. As an application, by substituting rigid analysis for complex analysis, it leads naturally to the -adic local functional equation at , which strongly resembles the complex one in Tate's thesis.
Cite
@article{arxiv.2201.08874,
title = {Note on $p$-adic Local Functional Equation},
author = {Luochen Zhao},
journal= {arXiv preprint arXiv:2201.08874},
year = {2022}
}
Comments
26 pages; revised version with {\S}B.1 rewritten; accepted by p-Adic Numbers, Ultrametric Analysis and Applications