Testing the Congruence Conjecture for Rubin-Stark elements

JOURNAL OF NUMBER THEORY

卷:130

Article

Roblot, X. -F²  Solomon, D.¹ 

[1] Kings Coll London, London WC2R 2LS, England

[2] Univ Lyon 1, CNRS, Inst Camille Jordan, UMR 5208, F-69622 Villeurbanne, France

关键词: Rubin-Stark element;    Explicit reciprocity law;    Congruence conjecture;    L-function;    Hilbert symbol;    Real quadratic field;    PARI/GP;    PAR1;    Computation;   

DOI  :  10.1016/j.jnt.2010.02.002

来源: Elsevier

【 摘 要 】

The 'Congruence Conjecture' was developed by the second author in a previous paper [So3]. It provides a conjectural explicit reciprocity law for a certain element associated to an abelian extension of a totally real number field whose existence is predicted by earlier conjectures of Rubin and Stark. The first aim of the present paper is to design and apply techniques to investigate the Congruence Conjecture numerically. We then present complete verifications of the conjecture in 48 varied cases with real quadratic base fields. (c) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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