P-adic Analysis
A Short Course on Recent Work

Neal Koblitz (Author)

9780521280600, Cambridge University Press

Paperback, published 28 November 1980

168 pages
22.8 x 15.2 x 1 cm, 0.24 kg

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.

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.

Subject Areas: Probability & statistics [PBT]