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Weighted discrete universality of the Riemann zeta-function

    Antanas Laurinčikas Affiliation
    ; Darius Šiaučiūnas Affiliation
    ; Gediminas Vadeikis Affiliation

Abstract

It is well known that the Riemann zeta-function is universal in the Voronin sense, i.e., its shifts ζ(s + ), 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.

Keyword : approximation of analytic functions, Mergelyan theorem, Riemann zeta-function, universality, weak convergence

How to Cite
Laurinčikas, A., Šiaučiūnas, D., & Vadeikis, G. (2020). Weighted discrete universality of the Riemann zeta-function. Mathematical Modelling and Analysis, 25(1), 21-36. https://doi.org/10.3846/mma.2020.10436
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Jan 13, 2020
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