On the zeros and singularities of p−adic trace functions

Abstract

Given a prime number p we consider ${\mathbb{C}}_p$ the topological completion of the algebraic closure of the field of p-adic numbers with respect to the usual p-adic absolute value. In this paper, we point out new connections between zeros and singularities of the trace functions associated with arbitrary elements of ${\mathbb{C}}_p.$

Keywords:

• Krasner analytic functions
• local fields
• distributions

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 11S99