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

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Prerequisites

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

This course is a prerequisite or co-requisite for

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Description

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.

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