Abstract
Let be a totally real number field, and let be a finite prime of such that splits completely in the finite abelian extension of . Tate has proposed a conjecture [22, Conjecture 5.4] stating the existence of a -unit in with absolute values at the places above specified in terms of the values at zero of the partial zeta functions associated to . This conjecture is an analogue of Stark's conjecture, which Tate called the Brumer-Stark conjecture. Gross [12, Conjecture 7.6] proposed a refinement of the Brumer-Stark conjecture that gives a conjectural formula for the image of in , where denotes the completion of at and denotes the topological closure of the group of totally positive units of . We present a further refinement of Gross's conjecture by proposing a conjectural formula for the exact value of in
Citation
Samit Dasgupta. "Shintani zeta functions and Gross-Stark units for totally real fields." Duke Math. J. 143 (2) 225 - 279, 1 June 2008. https://doi.org/10.1215/00127094-2008-019
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