Geodesic
Universality of $L$-Dirichlet functions and~nontrivial zeros of the Riemann zeta-function
Sbornik. Mathematics, Tome 210 (2019) no. 12, pp. 1753-1773

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We prove a joint discrete universality theorem for Dirichlet $L$-functions concerning joint approximation of a tuple of analytic functions by shifts $L(s+ih\gamma_k, \chi_1),\dots,L(s+ih\gamma_k,\chi_r)$, where $0\gamma_1\gamma_2\dotsb$ is the sequence of imaginary parts of the nontrivial zeros of the Riemann zeta-function, $h$ is a fixed positive number, and $\chi_1,\dots,\chi_r$ are pairwise nonequivalent Dirichlet characters. We use a weak form of Montgomery's conjecture on the correlation of pairs of zeros of the Riemann zeta-function in the analysis. Moreover, we show the universality of certain compositions of Dirichlet $L$-functions with operators in the space of analytic functions. Bibliography: 31 titles.
Keywords: Montgomery's conjecture on correlation of pairs, Riemann zeta-function, Dirichlet $L$-function, nontrivial zeros, Voronin's theorem, universality. 
@article{SM_2019_210_12_a4,
     author = {A. Laurin\v{c}ikas and J. Petu\v{s}kinait\.{e}},
     title = {Universality of $L${-Dirichlet} functions and~nontrivial zeros of the {Riemann} zeta-function},
     journal = {Sbornik. Mathematics},
     pages = {1753--1773},
     publisher = {mathdoc},
     volume = {210},
     number = {12},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2019_210_12_a4/}
}
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A. Laurinčikas; J. Petuškinaitė. Universality of $L$-Dirichlet functions and~nontrivial zeros of the Riemann zeta-function. Sbornik. Mathematics, Tome 210 (2019) no. 12, pp. 1753-1773. http://geodesic.mathdoc.fr/item/SM_2019_210_12_a4/