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Shintani zeta functions and gross-stark units for totally real fields

Publication ,  Journal Article
Dasgupta, S
Published in: Duke Mathematical Journal
June 1, 2008

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 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.

Duke Scholars

Published In

Duke Mathematical Journal

DOI

ISSN

0012-7094

Publication Date

June 1, 2008

Volume

143

Issue

2

Start / End Page

225 / 279

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics
 

Citation

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Dasgupta, S. (2008). Shintani zeta functions and gross-stark units for totally real fields. Duke Mathematical Journal, 143(2), 225–279. https://doi.org/10.1215/00127094-2008-019
Dasgupta, S. “Shintani zeta functions and gross-stark units for totally real fields.” Duke Mathematical Journal 143, no. 2 (June 1, 2008): 225–79. https://doi.org/10.1215/00127094-2008-019.
Dasgupta S. Shintani zeta functions and gross-stark units for totally real fields. Duke Mathematical Journal. 2008 Jun 1;143(2):225–79.
Dasgupta, S. “Shintani zeta functions and gross-stark units for totally real fields.” Duke Mathematical Journal, vol. 143, no. 2, June 2008, pp. 225–79. Scopus, doi:10.1215/00127094-2008-019.
Dasgupta S. Shintani zeta functions and gross-stark units for totally real fields. Duke Mathematical Journal. 2008 Jun 1;143(2):225–279.
Journal cover image

Published In

Duke Mathematical Journal

DOI

ISSN

0012-7094

Publication Date

June 1, 2008

Volume

143

Issue

2

Start / End Page

225 / 279

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics