Arithmetic of L-functions [the 2009 IAS PCMI graduate summer school

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. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price. Pt. 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 -- Pt. 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 -- Pt. Iii. Analytic And Cohomological Methods -- Root Numbers -- Euler Systems And Kolyvagin Systems. Cristian Popescu, Karl Rubin, Alice Silverberg, Editors. Includes Bibliographical References.