Double Dirichlet Series over Function Fields
نویسندگان
چکیده
We construct a nite-dimensional vector space of functions of two complex variables attached to a smooth algebraic curve C over a nite eld Fq , q odd, and a level. These functions collect the analytic information about the cohomology of the curve and its quadratic twists that is encoded in the corresponding L-functions; they are double Dirichlet series in two independent complex variables s;w. We prove that these series satisfy a nite, non-abelian group of functional equations in the two complex variables (s; w) and are rational functions in q , q w with a speci ed denominator. The group is D6, the dihedral group of order 12.
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