Anderson's double complex and gamma monomials for rational 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...

On rational bounds for the gamma function

In the article, we prove that the double inequality [Formula: see text] holds for all [Formula: see text], we present the best possible constants λ and μ such that [Formula: see text] for all [Formula: see text], and we find the value of [Formula: see text] in the interval [Formula: see text] such that [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text], ...

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

The Gross Conjecture over Rational Function Fields

We study the Gross Conjecture on the cyclotomic function field extension k(Λf )/k where k = Fq(t) is the rational function field and f is a monic polynomial in Fq[t]. We show the conjecture in the Fermat curve case(i.e., when f = t(t− 1)) by direct calculation. We also prove the case when f is irreducible which is analogous to Weil’s reciprocity law. In the general case, we manage to show the w...