On Krasner analytic functions and the p-adic Mellin transform

Mellin transforms of p-adic Whittaker functions

Lipeomorphic Equivalence for P-adic Analytic Functions: a Comparison between Complex and P-adic Dynamics

Let K be a p-adic field, and suppose that f and g are germs of analytic functions on K which are tangent to the identity at 0. It is known that f and g are homeomorphically equivalent, meaning there is an invertible germ h so that h−1◦f ◦h = g. In this paper, we determine whether there exists such h which are lipeomorphisms, and moreover find the best possible Hölder estimate at 0. Our results ...

Analytic P-adic Cell Decomposition and P-adic Integrals

Roughly speaking, the semialgebraic cell decomposition theorem for p-adic numbers describes piecewise the p-adic valuation of p-adic polyno-mials (and more generally of semialgebraic p-adic functions), the pieces being geometrically simple sets, called cells. In this paper we prove a similar cell decomposition theorem to describe piecewise the valuation of analytic functions (and more generally...

Analytic p-adic L-functions for GL2: a summary

One of the most subtle and important invariants of a modular form f is its L-function L(s, f). For holomorphic modular forms, the basic analytic properties of their L-functions were established by Hecke, with Maass treating the real-analytic forms; their construction gave L(s, f) as a Mellin transform of f . In the early 70s, the existence of p-adic L-functions associated with classical modular...

Appendix. the Mellin Transform and Related Analytic Techniques

The Mellin transformation is a basic tool for analyzing the behavior of many important functions in mathematics and mathematical physics, such as the zeta functions occurring in number theory and in connection with various spectral problems. We describe it first in its simplest form and then explain how this basic definition can be extended to a much wider class of functions, important for many...