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Stark's Conjectures: Recent Work and New Directions
Edited by: David Burns, King's College, London, England, Cristian Popescu, University of California, San Diego, CA, Jonathan Sands, University of Vermont, Burlington, VT, and David Solomon, King's College, London, England
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Contemporary Mathematics
2004; 221 pp; softcover
Volume: 358
ISBN-10: 0-8218-3480-0
ISBN-13: 978-0-8218-3480-0
List Price: US$76
Member Price: US$60.80
Order Code: CONM/358
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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.

Readership

Graduate students and research mathematicians interested in number theory.

Table of Contents

  • C. D. Popescu -- Rubin's integral refinement of the abelian Stark conjecture
  • D. S. Dummit -- Computations related to Stark's conjecture
  • C. Greither -- Arithmetic annihilators and Stark-type conjectures
  • M. Flach -- The equivariant Tamagawa number conjecture: A survey
  • J. W. Sands -- Popescu's conjecture in multi-quadratic extensions
  • D. Solomon -- Abelian conjectures of Stark type in \(\mathbb{Z}_p\)-extensions of totally real fields
  • H. M. Stark -- The derivative of p-adic Dirichlet series at s=0
  • J. Tate -- Refining Gross's conjecture on the values of abelian \(L\)-functions
  • D. R. Hayes -- Stickleberger functions for non-abelian Galois extensions of global fields
  • B. Mazur and K. Rubin -- Introduction to Kolyvagin systems
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