Compositio Mathematica

On a Refined Stark Conjecture for Function Fields

a1 Department of Mathematics, University of Texas at Austin, Austin, TX 78712-1082, U.S.A. e mail

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We prove that a refinement of Stark‘s Conjecture formulated by Rubin in Ann. Inst Fourier 4 (1996) is true up to primes dividing the order of the Galois group, for finite, Abelian extensions of function fields over finite fields. We also show that in the case of constant field extensions, a statement stronger than Rubin‘s holds true.

Key Words: special values of Abelian L-functions; units; class groups; characteristic p-global fields..