LMS: 46 P Adic Analysis: A Short Course on Recent Work (London Mathematical Society Lecture Note Series)

Koblitz

ISBN 10: 0521280605 / ISBN 13: 9780521280600

Published by Cambridge University Press 2008-01-12, 2008

About this Item

Seller Inventory # 6666-IUK-9780521280600

Bibliographic Details

Title: LMS: 46 P Adic Analysis: A Short Course on ...

Publisher: Cambridge University Press 2008-01-12

Publication Date: 2008

Binding: Paperback

Condition: New

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:

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 author develops the properties of p-adic Dirichlet L-series using p-adic measures and integration.