Universality of zeta-functions of cusp forms and non-trivial zeros of the Riemann zeta-function - Balčiūnas, Aidas; Franckevič, Violeta; Garbaliauskienė, Virginija; Macaitienė, Renata; Rimkevičienė, Audronė (Mathematical Modelling and Analysis, 2021)
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.