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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Generalized Stark formulae over function fields


Author: Ki-Seng Tan
Journal: Trans. Amer. Math. Soc. 361 (2009), 2277-2304
MSC (2000): Primary 11S40; Secondary 11R42, 11R58
Published electronically: December 23, 2008
MathSciNet review: 2471918
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Abstract: We establish formulae of Stark type for the Stickelberger elements in the function field setting. Our result generalizes work of Hayes and a conjecture of Gross. It is used to deduce a $ p$-adic version of the Rubin-Stark Conjecture and the Burns Conjecture.


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Additional Information

Ki-Seng Tan
Affiliation: Department of Mathematics, National Taiwan University, Taipei 10764, Taiwan
Email: tan@math.ntu.edu.tw

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04830-7
PII: S 0002-9947(08)04830-7
Keywords: Stickelberger element, special values of $L$-functions, Stark Conjecture, conjecture of Gross, class numbers, local Leopoldt conjecture, Rubin's conjecture, conjecture of Rubin and Burns, regulators
Received by editor(s): June 26, 2006
Published electronically: December 23, 2008
Additional Notes: The author was supported in part by the National Science Council of Taiwan, NSC91-2115-M-002-001, NSC93-2115-M-002-007.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.