P-adic Analysis: A Short Course on Recent Work (London Mathematical Society Lecture Note Series, Series Number 46) - Softcover

Koblitz, Neal

Softcover

ISBN 10: 0521280605 ISBN 13: 9780521280600

Publisher: Cambridge University Press, 1980

Synopsis

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.

About this title

Book Description:

An introduction to recent work in the theory of numbers and its interrelation with algebraic geometry and analysis.

About this edition

• Publisher: Cambridge University Press
• Publication date: 1980
• ISBN 10: 0521280605
• ISBN 13: 9780521280600
• Binding: Paperback
• Edition number: 1
• Number of pages: 168