Extremal values of Dirichlet -functions in the half-plane of absolute convergence
We prove that for any real there are infinitely many values of with and such that The proof relies on an effective version of Kronecker’s approximation theorem.
Upper bounds for the density of universality
On the value-distribution of Epstein zeta-functions.
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 -Functions
We prove a new type of universality theorem for the Riemann zeta-function and other -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
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.
Limit theorems in the space of analytic functions for the Hurwitz zeta-function with an algebraic irrational parameter
We prove a limit theorem in the space of analytic functions for the Hurwitz zeta-function with algebraic irrational parameter.
Erratum: "On the number of prime divisors of the order of elliptic curves modulo p" (Acta Arith. 117 (2005), 341-352)
On the number of prime divisors of the order of elliptic curves modulo p
A Note on Moments of Zeta'(1/2+i Gamma)
Kettenbrüche als Summen ebensolcher
A note on moments of .
Simpson's paradox in the Farey sequence.
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