Lectures on Non-Archimedean Function Theory

TL;DR

This paper provides an overview of non-Archimedean function theory, covering analogs of classical complex analysis concepts, valuation polygons, value distribution, and Ahlfors Island theorems in a non-Archimedean context.

Contribution

It introduces foundational concepts and analogs of classical theorems in non-Archimedean analysis, expanding the theoretical framework of the field.

Findings

Development of non-Archimedean analogs of classical theorems

Introduction of valuation (Newton) polygons and their applications

Presentation of non-Archimedean value distribution theory

Abstract

Lecture 1 discusses non-Archimedean analogs of classical complex function theory based on the Schnirelman integral. Lecture 2 discusses valuation (Newton) polygons and their consequences and presents a non-Archimedean analog of the Poisson-Jensen formula. Lecture 3 introduces non-Archimedean value distribution theory. Lecture 4 presents an introduction to Benedetto's non-Archimedean analogs of the Ahlfors Island theorems.