Weighted discrete universality of the Riemann zeta-function

Abstract

It is well known that the Riemann zeta-function is universal in the Voronin sense, i.e., its shifts ζ(s + iτ), τ ∈ R, approximate a wide class of analytic functions. The universality of ζ(s) is called discrete if τ take values from a certain discrete set. In the paper, we obtain a weighted discrete universality theorem for ζ(s) when τ takes values from the arithmetic progression {kh : k ∈N} with arbitrary fixed h > 0. For this, two types of h are considered.

Keywords

• approximation of analytic functions
• Mergelyan theorem
• Riemann zeta-function
• universality
• weak convergence