Asymptotic properties of Dedekind zeta functions in families of number fields

Alexey Zykin

Displaying similar documents to “Asymptotic properties of Dedekind zeta functions in families of number fields”

On certain sums over ordinates of zeta-zeros

A. Ivić (2001)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

Similarity:

On zeta-functions associated to certain cusp forms. I

A. Laurinčikas, J. Steuding (2004)

Open Mathematics

Similarity:

In the paper the asymptotics for Dirichlet polynomials associated to certain cusp forms are obtained.

Oscillation of Mertens’ product formula

Harold G. Diamond, Janos Pintz (2009)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Mertens’ product formula asserts that $\prod_{p \leq x} (1 - \frac{1}{p}) log x \to e^{- γ}$ as $x \to \infty$ . Calculation shows that the right side of the formula exceeds the left side for $2 \leq x \leq 10^{8}$ . It was suggested by Rosser and Schoenfeld that, by analogy with Littlewood’s result on $π (x) - li x$ , this and a complementary inequality might change their sense for sufficiently large values of $x$ . We show this to be the case.

A multiple sum involving the Möbius function.

Motohashi, Yoichi (2004)

Publications de l'Institut Mathématique. Nouvelle Série

Similarity:

On a problem of Fujii concerning Riemann's $ζ$ -function.

Puchta, J.-C. (2001)

Acta Mathematica Universitatis Comenianae. New Series

Similarity:

On some mean value results involving |zeta(1/2+ it)|

A. Ivić (2003)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

Similarity:

Another relation between π, e, γ and ζ(n).

Luis J. Boya (2008)

RACSAM

Similarity:

On some mean value results involving $| ζ (1 / 2 + i t) |$ .

Ivić, A. (2003)

Bulletin. Classe des Sciences Mathématiques et Naturelles. Sciences Mathématiques

Similarity:

Gaps between zeros of the derivative of the Riemann $ξ$ -function

Hung Manh Bui (2010)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Assuming the Riemann hypothesis, we investigate the distribution of gaps between the zeros of $ξ^{'} (s)$ . We prove that a positive proportion of gaps are less than $0.796$ times the average spacing and, in the other direction, a positive proportion of gaps are greater than $1.18$ times the average spacing. We also exhibit the existence of infinitely many normalized gaps smaller (larger) than $0.7203$ ( $1.5$ , respectively).