P-Adic Analysis: A Short Course on Recent Work

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.

Author: Neal Koblitz
Publisher: Cambridge University Press
Published: 11/28/1980
Pages: 168
Binding Type: Paperback
Weight: 0.59lbs
Size: 9.06h x 6.10w x 0.43d
ISBN: 9780521280600

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