Multiple Dirichlet Series over Rational Function Fields
نویسنده
چکیده
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.
منابع مشابه
Twisted Weyl Group Multiple Dirichlet Series Over the Rational Function Field
TWISTED WEYL GROUP MULTIPLE DIRICHLET SERIES OVER THE RATIONAL FUNCTION FIELD SEPTEMBER 2013 HOLLEY A. FRIEDLANDER, B.A., UNIVERSITY OF VERMONT M.S., UNIVERSITY OF MASSACHUSETTS AMHERST Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor Paul E. Gunnells Let K be a global field. For each prime p of K, the p-part of a multiple Dirichlet series defined over K is a generating functio...
متن کاملHYPERTRANSCENDENTAL FORMAL POWER SERIES OVER FIELDS OF POSITIVE CHARACTERISTIC
Let $K$ be a field of characteristic$p>0$, $K[[x]]$, the ring of formal power series over $ K$,$K((x))$, the quotient field of $ K[[x]]$, and $ K(x)$ the fieldof rational functions over $K$. We shall give somecharacterizations of an algebraic function $fin K((x))$ over $K$.Let $L$ be a field of characteristic zero. The power series $finL[[x]]$ is called differentially algebraic, if it satisfies...
متن کاملWeyl Group Multiple Dirichlet Series of Type A2
A Weyl group multiple Dirichlet series is a Dirichlet series in several complex variables attached to a root system Φ. The number of variables equals the rank r of the root system, and the series satisfies a group of functional equations isomorphic to the Weyl group W of Φ. In this paper we construct a Weyl group multiple Dirichlet series over the rational function field using n order Gauss sum...
متن کاملWeyl Group Multiple Dirichlet
Abstract. A Weyl group multiple Dirichlet series is a Dirichlet series in several complex variables attached to a root system Φ. The number of variables equals the rank r of the root system, and the series satisfies a group of functional equations isomorphic to the Weyl group W of Φ. In this paper we construct a Weyl group multiple Dirichlet series over the rational function field using n order...
متن کاملec 2 00 6 ON THE p - PARTS OF QUADRATIC WEYL GROUP MULTIPLE DIRICHLET SERIES
Let Φ be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Φ is a Dirichlet series in r complex variables s1, . . . , sr, initially converging for R(si) sufficiently large, which has meromorphic continuation to C and satisfies functional equations under the transformations of C corresponding to the Weyl group of Φ. Two constructions of such series are available, one [1...
متن کامل