Testing the Congruence Conjecture for Rubin-Stark elements

TY - JOUR

T1 - Testing the Congruence Conjecture for Rubin-Stark elements

AU - Roblot, X. -F

AU - Solomon, D.

PY - 2010/6

Y1 - 2010/6

N2 - 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.

AB - 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.

U2 - 10.1016/j.jnt.2010.02.002

DO - 10.1016/j.jnt.2010.02.002

M3 - Article

VL - 130

SP - 1374

EP - 1398

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 6

ER -