P-adic Analysis: A Short Course on Recent Work available in Paperback
- Pub. Date:
- Cambridge University Press
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 ContentsPreface; 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.