P-Adic Analysis : A Short Course on Recent Work
Overview
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.
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Details
- ISBN-13: 9780521280600
- ISBN-10: 0521280605
- Publisher: Cambridge University Press
- Publish Date: November 1980
- Dimensions: 9.06 x 6.1 x 0.43 inches
- Shipping Weight: 0.59 pounds
- Page Count: 168
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