Generalized Stark formulae over function fields

Author:

Tan Ki-Seng

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 p -adic version of the Rubin-Stark Conjecture and the Burns Conjecture.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference34 articles.

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2. On Tate’s refinement for a conjecture of Gross and its generalization;Aoki, Noboru;J. Th\'{e}or. Nombres Bordeaux,2004

3. [Bun02] D. Burns, On relations between derivatives of abelian 𝐿-functions at 𝑠=0, preprint, 2002.

4. On the values of equivariant zeta functions of curves over finite fields;Burns, David;Doc. Math.,2004

5. Congruences between derivatives of abelian 𝐿-functions at 𝑠=0;Burns, David;Invent. Math.,2007

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1. Congruences between derivatives of geometric L-functions;Inventiones mathematicae;2010-11-03

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