Universality of zeta-functions of cusp forms and non-trivial zeros of the Riemann zeta-function
DOI: https://doi.org/10.3846/mma.2021.12447Abstract
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+iγkh,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.
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Montgomery pair correlation conjecture, Riemann zeta-function, zeta-function of cusp form, universality.How to Cite
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