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Arithmetic of L-functions

By: Contributor(s): Material type: TextTextLanguage: English Series: IAS/Park City mathematics series ; Vol. 18Publication details: American Mathematical Society Rhode Island Institute for Advanced Study 2011Description: xiv, 499p. illISBN:
  • 9780821853207 (HB)
  • 0821853201 (HB)
Subject(s):
Contents:
Part I. Stark’s conjecture Stark’s basic conjecture The origin of the “Stark conjectures” Integral and p-adic refinements of the abelian Stark conjecture Special values of L-functions at negative integers An introduction to the equivariant Tamagawa number conjecture: The relation to Stark’s conjecture Part II. Birch and Swinnerton-Dyer conjecture Introduction to elliptic curves Lectures on the conjecture of Birch and Swinnerton-Dyer Elliptic curves over function fields Heegner’s proof Complex multiplication: A concise introduction The equivariant Tamagawa number conjecture and the Birch-Swinnerton-Dyer conjecture Part III. Analytic and cohomological methods Root numbers Euler systems and Kolyvagin systems
Summary: The overall theme of the 2009 IAS/PCMI Graduate Summer School was connections between special values of L -functions and arithmetic, especially the Birch and Swinnerton-Dyer Conjecture and Stark's Conjecture. These conjectures are introduced and discussed in depth, and progress made over the last 30 years is described. This volume contains the written versions of the graduate courses delivered at the summer school. It would be a suitable text for advanced graduate topics courses on the Birch and Swinnerton-Dyer Conjecture and/or Stark's Conjecture. The book will also serve as a reference volume for experts in the field. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute.
Item type: BOOKS
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IMSc Library 511.331 POP (Browse shelf(Opens below)) Available 66555

Includes bibliography (p. 499) and references.

Part I. Stark’s conjecture
Stark’s basic conjecture
The origin of the “Stark conjectures”
Integral and p-adic refinements of the abelian Stark conjecture
Special values of L-functions at negative integers
An introduction to the equivariant Tamagawa number conjecture: The relation to Stark’s conjecture

Part II. Birch and Swinnerton-Dyer conjecture
Introduction to elliptic curves
Lectures on the conjecture of Birch and Swinnerton-Dyer
Elliptic curves over function fields
Heegner’s proof
Complex multiplication: A concise introduction
The equivariant Tamagawa number conjecture and the Birch-Swinnerton-Dyer conjecture

Part III. Analytic and cohomological methods
Root numbers
Euler systems and Kolyvagin systems

The overall theme of the 2009 IAS/PCMI Graduate Summer School was connections between special values of L

-functions and arithmetic, especially the Birch and Swinnerton-Dyer Conjecture and Stark's Conjecture. These conjectures are introduced and discussed in depth, and progress made over the last 30 years is described. This volume contains the written versions of the graduate courses delivered at the summer school. It would be a suitable text for advanced graduate topics courses on the Birch and Swinnerton-Dyer Conjecture and/or Stark's Conjecture. The book will also serve as a reference volume for experts in the field.

Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute.

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The Institute of Mathematical Sciences, Chennai, India