Math @ Duke

Publications [#338518] of Samit Dasgupta
Papers Published
 Dasgupta, S, Shintani zeta functions and grossstark units for totally real fields,
Duke Mathematical Journal, vol. 143 no. 2
(June, 2008),
pp. 225279, Duke University Press [doi]
(last updated on 2022/01/25)
Abstract: 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 punit 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 BrumerStark conjecture. Gross [12, Conjecture 7.6] proposed a refinement of the BrumerStark conjecture that gives a conjectural formula for the image of u in Fpx/Ê, where FP denotes the completion of F at p and Ê 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 Fpx.


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