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A Weighted Universality Theorem for Periodic Zeta-Functions

    Renata Macaitienė Affiliation
    ; Mindaugas Stoncelis Affiliation
    ; Darius Šiaučiūnas Affiliation

Abstract

The periodic zeta-function ζ(s; a), s = σ + it is defined for σ > 1 by the Dirichlet series with periodic coefficients and is meromorphically continued to the whole complex plane. It is known that the function ζ(s; a), for some sequences a of coefficients, is universal in the sense that its shifts ζ(s + iτ ; a), τ ∈ R, approximate a wide class of analytic functions. In the paper, a weighted universality theorem for the function ζ(s; a) is obtained.

Keyword : Hurwitz zeta-function, Mergelyan theorem, periodic zeta-function, universality

How to Cite
Macaitienė, R., Stoncelis, M., & Šiaučiūnas, D. (2017). A Weighted Universality Theorem for Periodic Zeta-Functions. Mathematical Modelling and Analysis, 22(1), 95-105. https://doi.org/10.3846/13926292.2017.1269373
Published in Issue
Jan 11, 2017
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This work is licensed under a Creative Commons Attribution 4.0 International License.