URS AND URSIMS FOR P-ADIC MEROMORPHIC FUNCTIONS INSIDE A DISC

RATIONAL DECOMPOSITIONS OF p-ADIC MEROMORPHIC FUNCTIONS

Let K be a non archimedean algebraically closed field of characteristic π, complete for its ultrametric absolute value. In a recent paper by Escassut and Yang ([6]) polynomial decompositions P (f) = Q(g) for meromorphic functions f , g on K (resp. in a disk d(0, r−) ⊂ K) have been considered, and for a class of polynomials P , Q, estimates for the Nevanlinna function T (ρ, f) have been derived....

Meromorphic Continuation of L-functions of P-adic Representations

open p - adic disc

This paper investigates Galois branched covers of the open p-adic disc and their reductions to characteristic p. Using the field of norms functor of Fontaine and Wintenberger, we show that the special fiber of a Galois cover is determined by arithmetic and geometric properties of the generic fiber and its characteristic zero specializations. As applications, we derive a criterion for good reduc...

p-ADIC PERIODS, p-ADIC L-FUNCTIONS, AND THE p-ADIC UNIFORMIZATION OF SHIMURA CURVES

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 ...