An introduction to the theory of local zeta functions
Author(s)
Bibliographic Information
An introduction to the theory of local zeta functions
（AMS/IP studies in advanced mathematics, v. 14）
American Mathematical Society , International Press, c2000
- : pbk
Available at / 42 libraries
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
: pbkS||AMSIP||14200021321905
-
No Libraries matched.
- Remove all filters.
Note
Includes bibliographical references (p. 227-230) and index
Description and Table of Contents
- Volume
-
ISBN 9780821820155
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.
- Volume
-
: pbk ISBN 9780821829073
Description
This book is an introductory presentation to the theory of local zeta functions. Viewed as distributions, and mostly in the archimedean case, local zeta functions are also called complex powers. The volume contains major results on analytic and algebraic properties of complex powers by Atiyah, Bernstein, I. M. Gelfand, S. I. Gelfand, and Sato. Chapters devoted to $p$-adic local zeta functions present Serre's structure theorem, a rationality theorem, and many examples found by the author. The presentation concludes with theorems by Denef and Meuser. Information for our distributors: Titles in this series are co-published with International Press, Cambridge, MA.
Table of Contents
Preliminaries Implicit function theorems and $K$-analytic manifolds Hironaka's desingularization theorem Bernstein's theory Archimedean local zeta functions Prehomogeneous vector spaces Totally disconnected spaces and $p$-adic manifolds Local zeta functions ($p$-adic case) Some homogeneous polynomials Computation of $Z(s)$ Theorems of Denef and Meuser Bibliography Index.
by "Nielsen BookData"