Stark's Conjectures: Recent Work and New Directions (Contemporary Mathematics)

Stark's Conjectures: Recent Work and New Directions (Contemporary Mathematics)

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Description

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.

Contents

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

Product Details

  • ISBN13: 9780821834800
  • Format: Paperback
  • ID: 9780821834800
  • ISBN10: 0821834800

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