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Arithmetic of $L$-functions

About this Title

Cristian Popescu, University of California, San Diego, La Jolla, CA, Karl Rubin, University of California, Irvine, Irvine, CA and Alice Silverberg, University of California, Irvine, Irvine, CA, Editors

Publication: IAS/Park City Mathematics Series
Publication Year: 2011; Volume 18
ISBNs: 978-0-8218-5320-7 (print); 978-1-4704-1632-4 (online)
DOI: https://doi.org/10.1090/pcms/018
MathSciNet review: MR2882750
MSC: Primary 11-06

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Table of Contents

Front/Back Matter

• View this volume's front and back matter

Chapters

• Introduction

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

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