P-adic Analysis
A Short Course on Recent Work
1st Edition
Published on 4. February 2011
978-0-511-89206-6 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises
File size
25,79 MB
ISBN-13
978-0-511-89206-6 (9780511892066)
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Schweitzer Classification
Other editions
Additional editions
Book
11/1980
Cambridge University Press
€66.20
Shipment within 15-20 days
Content
Preface; 1. Basics; 2. p-adic functions, l-functions and r-functions; 3. Gauss sums and the p-adic gamma function; 4. p-adic regulators; Appendix; Bibliography; Index.
