Introduction to Analytic Functions in p-adic Analysis

The book first explains the main properties of analytic functions in order to use them in the study of various problems in p-adic value distribution.

Properties of p-adic Transcendental Numbers

Certain properties of p-adic transcendental numbers are examined such as order and type of transcendence, with problems on p-adic exponentials.

Lazard's Problem and Analytic Functions

Lazard's problem for analytic functions inside a disk is explained.

p-adic Meromorphic Functions

P-adic meromorphics are studied.

Range Uniqueness and the Ultrametric Corona Problem

Sets of range uniqueness in a p-adic field are examined. The ultrametric Corona problem is studied.

Injective Analytic Elements and p-adic Nevanlinna Theory

Injective analytic elements are characterized. The p-adic Nevanlinna theory is described and many applications are given: p-adic Hayman conjecture, Picard's values for derivatives, small functions, branched values, growth of entire functions, problems of uniqueness, URSCM and URSIM, functions of uniqueness, sharing value problems, Nevanlinna theory in characteristic p>0, p-adic Yosida's equation.