Stark's Conjectures: Recent Work and New Directions

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Brand new. We distribute directly for the publisher. A conference was organized to discuss research in variational methods as applied to nonlinear elliptic PDE. This volume ... resulted from that gathering. Included are both survey and research papers that address important open questions and offer suggestions on analytical and numerical techniques for solving those open problems.It is suitable for graduate students and research mathematicians interested in elliptic partial differential equations. Read more Show Less

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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.

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Product Details

  • ISBN-13: 9780821834800
  • Publisher: American Mathematical Society
  • Publication date: 9/16/2004
  • 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 conjecture 1
Computations related to Stark's conjecture 37
Arithmetic annihilators and Stark-type conjectures 55
The equivariant Tamagawa number conjecture : a survey 79
Popescu's conjecture in multi-quadratic extensions 127
Abelian conjectures of Stark type in Z[subscript p] -extensions of totally real fields 143
The derivative of p-adic Dirichlet series at s = 0 179
Refining Gross's conjecture on the values of abelian L-functions 189
Stickelberger functions for non-abelian Galois extensions of global fields 193
Introduction to Kolyvagin systems 207
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