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AMS/IP Studies in Advanced Mathematics

Volume 14

An Introduction to the Theory of Local Zeta Functions

Original Publication: 2000

Publisher: American Mathematical Society / International Press

Language: English

Paperback

232 pages

Description

This book is an introductory presentation to the theory of local zeta functions. As distributions, and mostly in the archimedian case, local zeta functions are called complex powers.

The volume contains major results on complex powers by Atiyah, Bernstein, I. M. Gelfand, and S. I. Gelfand. Also included are related results by Sato. The section on $p$-adic local zeta functions presents Serre's structure theorem, a rationality theorem and many examples by the author. It concludes with theorems by Denef and Meuser.

Prerequisites for understanding the text include basic courses in algebra, calculus, complex analysis, and general topology. The book follows the usual pattern of progress in mathematics: examples are given, conjectures follow, conjectures are developed into theorems.

This book is accessible and self-contained. Results illustrate the unity of mathematics by gathering important theorems from algebraic geometry and singularity theory, number theory, algebra, topology, and analysis. The ideas are then employed in essential ways to prove the theorems.

This volume is part of the AMS/IP Studies in Advanced Mathematics book series.

Publications

Pub. Date

ISBN-13

ISBN-10

Medium

Binding

Size, Etc.

Status

List Price

2015 Jan

9780821829073

0821829076

Print

paperback

In Print

2002

9780821888186

0821888188

Print

Out of Print

2000

9780821820155

082182015X

Print

hardcover

In Print

US$49.00