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Universality of zeta-functions of cusp forms and non-trivial zeros of the Riemann zeta-function

    Aidas Balčiūnas Affiliation
    ; Violeta Franckevič Affiliation
    ; Virginija Garbaliauskienė Affiliation
    ; Renata Macaitienė   Affiliation
    ; Audronė Rimkevičienė Affiliation

Abstract

It is known that zeta-functions ζ(s,F) of normalized Hecke-eigen cusp forms F are universal in the Voronin sense, i.e., their shifts ζ(s + iτ,F), τ ∈ R, approximate a wide class of analytic functions. In the paper, under a weak form of the Montgomery pair correlation conjecture, it is proved that the shifts ζ(s+kh,F), where γ1 < γ2 < ... is a sequence of imaginary parts of non-trivial zeros of the Riemann zeta function and h > 0, also approximate a wide class of analytic functions.

Keyword : Montgomery pair correlation conjecture, Riemann zeta-function, zeta-function of cusp form, universality.

How to Cite
Balčiūnas, A., Franckevič, V., Garbaliauskienė, V., Macaitienė, R., & Rimkevičienė, A. (2021). Universality of zeta-functions of cusp forms and non-trivial zeros of the Riemann zeta-function. Mathematical Modelling and Analysis, 26(1), 82-93. https://doi.org/10.3846/mma.2021.12447
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Jan 18, 2021
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