P-adic Analysis: A Short Course on Recent Work

by Neal Koblitz

• ISBN13: 9780521280600
• ISBN10: 0521280605
• Format: Paperback
• Copyright: 1980-11-28
• Publisher: Cambridge University Press

Summary

This introduction to recent work in p-adic analysis and number theory will make accessible to a relatively general audience the efforts of a number of mathematicians over the last five years. After reviewing the basics (the construction of p-adic numbers and the p-adic analog of the complex number field, power series and Newton polygons), the author develops the properties of p-adic Dirichlet L-series using p-adic measures and integration. p-adic gamma functions are introduced, and their relationship to L-series is explored. Analogies with the corresponding complex analytic case are stressed. Then a formula for Gauss sums in terms of the p-adic gamma function is proved using the cohomology of Fermat and Artin-Schreier curves. Graduate students and research workers in number theory, algebraic geometry and parts of algebra and analysis will welcome this account of current research.

Table of Contents

Preface

1. Basics

2. p-acid functions, l-functions and r-functions

3. Gauss sums and the p-acid gamma function

4. p-acid regulators

Appendix

Bibliography

Index.