Dedekind zeta函数与Dedekind和

DEDEKIND ZETA FUNCTIONSAND QUANTUM STATISTICAL MECHANICSPaula

Dedekind Zeta Functions and the Complexity of Hilbert’s Nullstellensatz

Let HN denote the problem of determining whether a system of multivariate polynomials with integer coefficients has a complex root. It has long been known that HN∈P =⇒ P=NP and, thanks to recent work of Koiran, it is now known that the truth of theGeneralized Riemann Hypothesis (GRH) yields the implication HN 6∈P =⇒ P 6=NP. We show that the assumption of GRH in the latter implication can be rep...

Computing the residue of the Dedekind zeta function

Assuming the Generalized Riemann Hypothesis, Bach has shown that one can calculate the residue of the Dedekind zeta function of a number field K by a clever use of the splitting of primes p < X, with an error asymptotically bounded by 8.33 logΔK/( √ X logX), where ΔK is the absolute value of the discriminant of K. Guided by Weil’s explicit formula and still assuming GRH, we make a different use...

ϕ-ALMOST DEDEKIND RINGS AND $\Phi$-ALMOST DEDEKIND MODULES

The purpose of this paper is to introduce some new classes of rings and modules that are closely related to the classes of almost Dedekind domains and almost Dedekind modules. We introduce the concepts of $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules and study some properties of this classes. In this paper we get some equivalent conditions for $\phi$-almost Dedekind rings and ...

Localization of the first zero of the Dedekind zeta function

Using Weil’s explicit formula, we propose a method to compute low zeros of the Dedekind zeta function. As an application of this method, we compute the first zero of the Dedekind zeta function associated to totally complex fields of degree less than or equal to 30 having the smallest known discriminant.