P-Adic Analysis

A Short Course on Recent Work

von Neal Koblitz

168 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Themen: Mathematik und Naturwissenschaften Mathematik Zahlentheorie
• ISBN: 9780521280600
• Sprache: Englisch
• Erscheinungsdatum: 15.05.2004
• Größe: 229 x 152 mm
• Verlag: Cambridge University Press
• Herausgegeben von: N. J. Hitchin, J. W. S. Cassels