On higher order Stickelberger-type theorems

JOURNAL OF NUMBER THEORY

卷:133

Article

Macias Castillo, Daniel

关键词: Stickelberger's theorem;    Stark's conjecture;    L-functions;    Annihilation;    Class groups;   

DOI  :  10.1016/j.jnt.2013.02.015

来源: Elsevier

【 摘 要 】

We discuss an explicit refinement of Rubin's integral version of Stark's conjecture. We prove that this refinement is a consequence of the relevant case of the Equivariant Tamagawa Number Conjecture of Burns and Flach, hence obtaining a full proof in several important cases. We also derive several explicit consequences of this refinement concerning the annihilation as Galois modules of ideal class groups by explicit elements constructed from the values of higher order derivatives of Dirichlet L-functions. We finally describe the relation between our approach and those found in recent work of Emmons and Popescu and of Buckingham. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free