Neal Koblitz

P-adic Analysis (eBook, PDF)

A Short Course on Recent Work

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 28. November 1980
• Englisch
• ISBN-13: 9780511892066
• Artikelnr.: 38186057

Inhaltsangabe

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.