Abstract
The Riemann zeta-function and the Hurwitz zeta-function with transcendental or rational parameter are universal in the sense of Voronin: their shifts approximate broad classes of analytic functions. The universality of the Hurwitz zeta-function with an algebraic irrational parameter is an open problem since 1979. Mishou proved the joint universality of the Riemann zeta-function and the Hurwitz zeta-function with transcendental parameter. Mishou’s theorem with an algebraic irrational parameter is also an open problem. Here we obtain first results in this direction. We prove that there exists a nonempty closed subset of a two-dimensional set of analytic functions such that every pair in it is approximated by the shifts mentioned.
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Russian Text © The Author(s), 2019, published in Sibirskii Matematicheskii Zhurnal, 2019, Vol. 60, No. 6, pp. 1379–1388.
The research was funded by the European Social Fund according to the activity “Improvement of Researchers’ Qualification by Implementing World-Class R&D Projects” (Grant 09.3.3—LMT—K—712—01—0037).
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Laurinčikas, A. On the Mishou Theorem with an Algebraic Parameter. Sib Math J 60, 1075–1082 (2019). https://doi.org/10.1134/S0037446619060144
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DOI: https://doi.org/10.1134/S0037446619060144