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  3. P-adic Analysis
  • Cited by 80
Publisher:
Cambridge University Press
Online publication date:
October 2009
Print publication year:
1980
Online ISBN:
9780511526107
DOI:
https://doi.org/10.1017/CBO9780511526107
Subjects:
Mathematics (general), Mathematics, Number Theory
Series:
London Mathematical Society Lecture Note Series (46)
Information

Book description

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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