Mathematische Annalen

, Volume 349, Issue 2, pp 301–343 | Cite as

Nonvanishing of Hecke L-functions and the Bloch–Kato conjecture

Article

Abstract

In this paper we study the central values of L-functions associated to a large class of algebraic Hecke characters of imaginary quadratic fields. When these central values are nonzero, the Bloch–Kato conjecture predicts an exact formula for the algebraic parts of the central values in terms of periods and arithmetic data, most notably the Selmer groups corresponding to the Hecke characters. We investigate the nonvanishing of these central values, and prove the p-part of the Bloch–Kato conjecture in these cases for primes p which split in K.

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Authors and Affiliations

  1. 1.School of MathematicsVictoria University of WellingtonWellingtonNew Zealand
  2. 2.Department of MathematicsUniversity of WisconsinMadisonUSA

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