Double Dirichlet series over function fields
نویسندگان
چکیده
منابع مشابه
Double Dirichlet Series over Function Fields
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. W...
متن کاملMultiple Dirichlet Series over Rational Function Fields
We explicitly compute some double Dirichlet series constructed from n order Gauss sums over rational function fields. These turn out to be rational functions in q−s1 and q−s2 , where q is the size of the constant field. Key use is made of the group of 6 functional equations satisfied by these series.
متن کاملTheta Series, Eisenstein Series and Poincaré Series over Function Fields
We construct analogues of theta series, Eisenstein series and Poincaré series for function fields of one variable over finite fields, and prove their basic properties.
متن کاملZeros of Dirichlet L-functions over Function Fields
Random matrix theory has successfully modeled many systems in physics and mathematics, and often analysis in one area guides development in the other. Hughes and Rudnick computed 1-level density statistics for low-lying zeros of the family of primitive Dirichlet L-functions of fixed prime conductor Q, as Q→∞, and verified the unitary symmetry predicted by random matrix theory. We compute 1and 2...
متن کاملSubconvexity for a Double Dirichlet Series
For two real characters ψ, ψ of conductor dividing 8 define Z(s,w;ψ, ψ′) := ζ2(2s+ 2w − 1) X d odd L2(s, χdψ)ψ (d) dw where χd = “
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2004
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x03000848