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On the value-distribution of Epstein zeta-functions.

Jörn Steuding — 2007

Publicacions Matemàtiques

We investigate the value-distribution of Epstein zeta-functions ζ(s; Q), where Q is a positive definite quadratic form in n variables. We prove an asymptotic formula for the number of c-values, i.e., the roots of the equation ζ(s; Q) = c, where c is any fixed complex number. Moreover, we show that, in general, these c-values are asymmetrically distributed with respect to the critical line Re s =n/4. This complements previous results on the zero-distribution. [Proceedings...

Ergodic Universality Theorems for the Riemann Zeta-Function and other L -Functions

Jörn Steuding — 2013

Journal de Théorie des Nombres de Bordeaux

We prove a new type of universality theorem for the Riemann zeta-function and other L -functions (which are universal in the sense of Voronin’s theorem). In contrast to previous universality theorems for the zeta-function or its various generalizations, here the approximating shifts are taken from the orbit of an ergodic transformation on the real line.

Upper bounds for the density of universality. II

Jörn Steuding — 2005

Acta Mathematica Universitatis Ostraviensis

We prove explicit upper bounds for the density of universality for Dirichlet series. This complements previous results [15]. Further, we discuss the same topic in the context of discrete universality. As an application we sharpen and generalize an estimate of Reich concerning small values of Dirichlet series on arithmetic progressions in the particular case of the Riemann zeta-function.

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