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P-adic Analysis
Neal Koblitz
其他書名
A Short Course on Recent Work
出版Cambridge University Press, 1980-11-28
主題Mathematics / Number TheoryMathematics / Probability & Statistics / GeneralMathematics / Mathematical Analysis
ISBN05212806059780521280600
URLhttp://books.google.com.hk/books?id=4kTHgCT52lgC&hl=&source=gbs_api
EBookSAMPLE
註釋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.