Antanas Laurinčikas Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225 Vilnius, Lithuania

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Let 0 < γ1 < γ2 < ··· ⩽ ··· be the imaginary parts of non-trivial zeros of the Riemann zeta-function. In the paper, we consider the approximation of analytic functions by shifts of the Hurwitz zeta-function ζ(s + kh, α), h > 0, with parameter α such that the set {log(m + α): m0} is linearly independent over the field of rational numbers. For this, a weak form of the Montgomery conjecture on the pair correlation of {γk} is applied.

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    Laurinčikas, A., On discrete universality of the Hurwitz zeta-function, Results Math. 72 (2017) no.1–2, 907–917.

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    Laurinčikas, A. and Garunkˇstis, R., The Lerch Zeta-Function, Kluwer Academic Publishers, Dordrecht, Boston, London (2002).

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    Laurinčikas, A.ˇ and Macaitiene, R.˙ , The discrete universality of the periodic Hurwitz zeta-function, Integral Tranforms Spec. Funct., 20 (2009) no. 9–10, 673686.

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    Laurinčikas, A.ˇ and Meśka, L., On the modification of the universality of Hurwitz zeta-functions, Nonlinear Analysis: Model. Control, 21 (2016) no. 4, 564576.

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    Steuding, J., The roots of the equation ζ(s) = a are uniformly distributed modulo one, in: Anal. Probab. Methods Number Theory (eds. A. Laurincikasˇ et al., TEV, Vilnius (2012), 243249.

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