P-Adic Analysis : A Short Course on Recent Work

Neal Koblitz

ISBN 10: 0521280605 / ISBN 13: 9780521280600

Published by Cambridge University Press, 1980

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9780521280600

Bibliographic Details

• Title: P-Adic Analysis : A Short Course on Recent Work
• Publisher: Cambridge University Press
• Publication Date: 1980
• Language: English
• ISBN 10: 0521280605
• ISBN 13: 9780521280600
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 229W x 152H x 9D millimeters 229 millimeters width by 152 millimeters height by 9 millimeters depth
• Weight: 254 grams

About this title

Synopsis

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.

Book Description

An introduction to recent work in the theory of numbers and its interrelation with algebraic geometry and analysis.