P-adic Analysis [electronic resource] : A Short Course on Recent Work
- Neal Koblitz.
- Cambridge : Cambridge University Press, 1980.
- Physical description
- 1 online resource (168 p.) : digital, PDF file(s).
- London Mathematical Society lecture note series ; no. 46.
- Koblitz, Neal.
- 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.
- (source: Nielsen Book Data)
- Publisher's Summary
- 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.
(source: Nielsen Book Data)
- p-adic analysis.
- Publication date
- London Mathematical Society Lecture Note Series ; no. 46
- Title from publishers bibliographic system (viewed on 26 Apr 2012).
- Also issued in print format.
- Mode of access: World Wide Web.
- Available in another form
- Print version: 9780521280600
- 9780511526107 (ebook)
- 9780521280600 (paperback)