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 + iγkh, α), h > 0, with parameter α such that the set {log(m + α): m ∈
Bagchi, B., The statistical behaviour and universality properties of the Riemann zeta function and other allied Dirichlet series, Ph. D. Thesis, Indian Statistical Institute, Calcutta (1981).
Billingsley, P., Convergence of Probability Measures, Wiley, New York (1968).
Cassels, J. W. S., Footnote to a note of Davenport and Heilbronn, J. London Math. Soc, 36 (1961), 177–184.
Davenport, H. and Heilbronn, H., On the zeros of certain Dirichlet series, J. London Math. Soc, 11 (1936), 181–185.
Gonek, S. M., Analytic properties of zeta and L-functions, Ph. D. Thesis, University of Michigan (1979).
Hurwitz, A., Einige Eigenschaften der Dirichlet’schen FunktionenF ( s ) = ∑ ( D n ) 1 n s, die bei der Bestimmung der Klassenanzahlen binärer quadratischer Formen auftreten, Z. Math. Physik, 27 (1882), 86–101.
Kuipers, L. and Niederreiter, H., Uniform Distribution of Sequences, Pure and Applied Math., Wiley-Interscience, New York, London, Sydney (1974).
Laurinčikas, A., Limit Theorems for the Riemann Zeta-Function, Kluwer Academic Publishers, Dordrecht, Boston, London (1996).
Laurinčikas, A., The joint universality of Hurwitz zeta-functions, Siauliai Math.ˇ Semin., 3(11 ) (2008), 169–187.
Laurinčikas, A., A discrete universality theorem for the Hurwitz zeta-function, J. Number Theory, 143 (2014), 232–247.
Laurinčikas, A., On discrete universality of the Hurwitz zeta-function, Results Math. 72 (2017) no.1–2, 907–917.
Laurinčikas, A. and Garunkˇstis, R., The Lerch Zeta-Function, Kluwer Academic Publishers, Dordrecht, Boston, London (2002).
Laurinčikas, A.ˇ and Macaitiene, R.˙ , The discrete universality of the periodic Hurwitz zeta-function, Integral Tranforms Spec. Funct., 20 (2009) no. 9–10, 673–686.
Laurinčikas, A.ˇ and Meśka, L., On the modification of the universality of Hurwitz zeta-functions, Nonlinear Analysis: Model. Control, 21 (2016) no. 4, 564–576.
Matsumoto, K., A survey on the theory of universality for zeta and L-functions, in: Number Theory: Plowing and Starring Through High Wave Forms (eds. M. Kaneko ), Proc. 7th China-Japan Seminar, Fukuoka, 2013, Series Number Theory and Appl., vol. 11, World Sci. Publ. Co. (2015), 95–144.
Mergelyan, S. N., Uniform approximations of functions of a complex variable (Russian), Uspehi Matem. Nauk (N. S.), 7 (1952) no. 2(48), 31–122; English translation in Amer. Math. Soc. Translation 1954, (1954) no. 101, 99 pp.
Montgomery, H. L., Topics in Multiplicative Number Theory, Lecture Notes Math., vol. 227, Springer-Verlag, Berlin, Heidelberg, New York (1971).
Montgomery, H. L., The pair correlation of zeros of the zeta function, in: Analytic Number Theory (ed. H. G. Diamond) (St. Louis Univ., 1972), Proc. Sympos. Pure Math., vol. XXIV, Amer. Math. Soc., Providence (1973), 181–193.
Sander, J. and Steuding, J., Joint universality for sums and products of Dirichlet L-functions, Analysis, 26 no. 3 (2006), 295–312.
Sarason, D., Complex Function Theory, Amer. Math. Soc., Providence (2007).
Steuding, J., Value-Distribution of L-Functions, Lecture Notes Math., vol. 1877, Springer, Berlin, Heidelberg, New York (2007).
Steuding, J., The roots of the equation ζ(s) = a are uniformly distributed modulo one, in: Anal. Probab. Methods Number Theory (eds. A. Laurincikasˇ , TEV, Vilnius (2012), 243–249.
Titchmarsh, E. C., The Theory of the Riemann zeta-Function, Second edition, Edited by D. R. Heath-Brown, Clarendon Press, Oxford (1986).
Voronin, S. M., A theorem on the“universality”of the Riemann zeta-function (Russian), Izv. Akad. Nauk SSSR, Ser. Matem., 39 (1975) no. 3, 475–486; English translation in Math. USSR-Izv., 9 (1975) no. 3, 443–453.