P-Adic Analysis: A Short Course on Recent Work
(Book #46 in the London Mathematical Society Lecture Note Series)
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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.
Format:Paperback
Language:English
ISBN:0521280605
ISBN13:9780521280600
Release Date:November 1980
Publisher:Cambridge University Press
Length:168 Pages
Weight:0.55 lbs.
Dimensions:0.4" x 6.1" x 9.1"
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