Stark's Conjectures: Recent Work and New Directions

Stark's Conjectures: Recent Work and New Directions

by David Burns
     
 

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

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Overview

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.

Product Details

ISBN-13:
9780821834800
Publisher:
American Mathematical Society
Publication date:
09/16/2004
Series:
Contemporary Mathematics Series, #358
Pages:
221
Product dimensions:
72.50(w) x 10.25(h) x 7.50(d)

Table of Contents

Rubin's integral refinement of the abelian Stark conjecture1
Computations related to Stark's conjecture37
Arithmetic annihilators and Stark-type conjectures55
The equivariant Tamagawa number conjecture : a survey79
Popescu's conjecture in multi-quadratic extensions127
Abelian conjectures of Stark type in Z[subscript p] -extensions of totally real fields143
The derivative of p-adic Dirichlet series at s = 0179
Refining Gross's conjecture on the values of abelian L-functions189
Stickelberger functions for non-abelian Galois extensions of global fields193
Introduction to Kolyvagin systems207

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