P-adic Analysis : A Short Course on Recent Work / Neal Koblitz.

By: Koblitz, Neal [author.]Material type: TextTextSeries: London Mathematical Society Lecture Note Series ; no. 46Publisher: Cambridge : Cambridge University Press, 1980Description: 1 online resource (168 pages) : digital, PDF file(s)Content type: text Media type: computer Carrier type: online resourceISBN: 9780511526107 (ebook)Subject(s): p-adic analysisAdditional physical formats: Print version: : No titleDDC classification: 512/.74 LOC classification: QA241 | .K673Online resources: Click here to access online 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.
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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.

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