**Contemporary Mathematics**

Volume: 358;
2004;
221 pp;
Softcover

MSC: Primary 11;

Print ISBN: 978-0-8218-3480-0

Product Code: CONM/358

List Price: $80.00

Individual Member Price: $64.00

**Electronic ISBN: 978-0-8218-7948-1
Product Code: CONM/358.E**

List Price: $80.00

Individual Member Price: $64.00

# Stark’s Conjectures: Recent Work and New Directions

Share this page *Edited by *
*David Burns; Cristian Popescu; Jonathan Sands; David Solomon*

Stark's conjectures on the behavior of \(L\)-functions were formulated in the 1970s. Since then, these conjectures and their generalizations have been actively investigated. This has led to significant progress in algebraic number theory.

The current volume, based on the conference held at Johns Hopkins University (Baltimore, MD), represents the state-of-the-art research in this area. The first four survey papers provide an introduction to a majority of the recent work related to Stark's conjectures. The remaining six contributions touch on some major themes currently under exploration in the area, such as non-abelian and \(p\)-adic aspects of the conjectures, abelian refinements, etc. Among others, some important contributors to the volume include Harold M. Stark, John Tate, and Barry Mazur.

The book is suitable for graduate students and researchers interested in number theory.

#### Table of Contents

# Table of Contents

## Stark's Conjectures: Recent Work and New Directions

- Contents v6 free
- Preface vii8 free
- List of Participants ix10 free
- Rubin's integral refinement of the abelian Stark conjecture 112 free
- Computations related to Stark's conjecture 3748
- Arithmetic annihilators and Stark-type conjectures 5566
- The equivariant Tamagawa number conjecture: A survey 7990
- Popescu's conjecture in multi-quadratic extensions 127138
- Abelian conjectures of Stark type in Zp-extensions of totally real fields 143154
- The derivative of p-adic Dirichlet series at s = 0 179190
- Refining Gross's conjecture on the values of abelian L-functions 189200
- Stickelberger functions for non-abelian Galois extensions of global fields 193204
- Introduction to Kolyvagin systems 207218

#### Readership

Graduate students and research mathematicians interested in number theory.