Duke Mathematical Journal
- Duke Math. J.
- Volume 143, Number 2 (2008), 225-279.
Shintani zeta functions and Gross-Stark units for totally real fields
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
Duke Math. J., Volume 143, Number 2 (2008), 225-279.
First available in Project Euclid: 26 May 2008
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Dasgupta, Samit. Shintani zeta functions and Gross-Stark units for totally real fields. Duke Math. J. 143 (2008), no. 2, 225--279. doi:10.1215/00127094-2008-019. https://projecteuclid.org/euclid.dmj/1211819163