Double complex and gamma-monomials in global function fields

Algebraic Gamma Monomials and Double Coverings of Cyclotomic Fields

We investigate the properties of algebraic gamma monomials— that is, algebraic numbers which are expressible as monomials in special values of the classical gamma function. Recently Anderson has constructed a double complex SK, to compute H∗(±,U), where U is the universal ordinary distribution. We use the double complex to deduce explicit formulae for algebraic gamma monomials. We provide simpl...

Euler Systems in Global Function Fields

In this paper, the construction of Euler systems of cyclotomic units in a general global function fields is explained. As an application, an analogue of Gras' conjecture in a global function field is proved. 1. I n t r o d u c t i o n and n o t a t i o n s Kolyvagin [7] introduced his remarkable Euler systems to prove important new results on ideal class groups of nmnber felds. This method was ...

Krull's theory for the double gamma function

The Barnes’ G-function G(x) = 1/Γ2, satisfies the functional equation log G(x + 1) − log G(x) = log Γ(x). We complement W. Krull’s work in Bemerkungen zur Differenzengleichung g(x + 1)− g(x) = φ(x), Math. Nachrichten 1 (1948), 365-376 with additional results that yield a different characterization of the function G, new expansions and sharp bounds for G on x > 0 in terms of Gamma and Digamma fu...

A Double Inequality for Gamma Function

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...