Lectures on Non-Archimedean Function Theory

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.
Comment: Lecture notes from a short course in the Advanced School on p-Adic Analysis and Applications held at the Abdus Salam International Centre for Theoretical Physics, August 31 - September 11, 2009