1 June 2008 Shintani zeta functions and Gross-Stark units for totally real fields
Samit Dasgupta
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Duke Math. J. 143(2): 225-279 (1 June 2008). DOI: 10.1215/00127094-2008-019


Let F be a totally real number field, and let p be a finite prime of F such that p splits completely in the finite abelian extension H of F. Tate has proposed a conjecture [22, Conjecture 5.4] stating the existence of a p-unit u in H with absolute values at the places above p specified in terms of the values at zero of the partial zeta functions associated to H/F. 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 u in Fp×/E, where Fp denotes the completion of F at p and E denotes the topological closure of the group of totally positive units E of F. We present a further refinement of Gross's conjecture by proposing a conjectural formula for the exact value of u in Fp×


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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


Published: 1 June 2008
First available in Project Euclid: 26 May 2008

zbMATH: 1235.11102
MathSciNet: MR2420508
Digital Object Identifier: 10.1215/00127094-2008-019

Primary: 11R37 , 11R42
Secondary: 11R80

Rights: Copyright © 2008 Duke University Press


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Vol.143 • No. 2 • 1 June 2008
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