P-adic analysis
Subtitle: a short course on recent work
By: Neal Koblitz.
Series: London Mathematical Society lecture note series ; 46; London Mathematical Society lecture note series ;; 46.
Publisher: Cambridge University Press
Published: 1980
Place of publication: Cambridge [Eng.]; New York
Language: eng
Number of pages: 163
Subjects: p-adic analysis.
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.
Notes: Bibliography: p. 154-160.
Includes index.