MTH 528, Introduction to p-adic Analysis

Note: If this course is being taught this semester, more information can be found at the course home page.

Cross Listed



MTH 436 or 236, MTH 437 or 237, MTH 440 or 240, MTH 265

This course is a prerequisite or co-requisite for



We will study the p-adic number fields and discuss applications to number theory and topology.

Topics covered

Model for the p-adic integers as a fractal clock, Hensel’s Lemma, discussion of the p-adic numbers, their algebraic closure and algebraically closed completion. The theory of continuous functions on the p-adics and their Mahler expansions, differentiability and Volkenborn integration on the p-adics. The extension of complex analysis to the p-adics with applications to special functions such as the Morita Gamma function and to the study of Bernoulli numbers.