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P-Adic Analysis: A Short Course on Recent Work by Neal Koblitz, J. W. S. Cassels, N. J. Hitchin

P-Adic Analysis: A Short Course on Recent Work

by Neal Koblitz , J. W. S. Cassels , N. J. Hitchin
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Book cover type: Paperback
  • ISBN13: 9780521280600
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Publication Date:
  • Pages: 168
  • Original Price: USD 66.0
  • Language: English
  • Edition: N/A
  • Item Weight: 268 grams
  • BISAC Subject(s): Number Theory

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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