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This article is cited in 4 scientific papers (total in 4 papers)
On the mishou theorem with an algebraic parameter
A. P. Laurinčikas Faculty of Mathematics and Informatics, Vilnius University
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.
Received: 23.04.2019 Revised: 23.04.2019 Accepted: 15.05.2019
Citation:
A. P. Laurinčikas, “On the mishou theorem with an algebraic parameter”, Sibirsk. Mat. Zh., 60:6 (2019), 1379–1388; Siberian Math. J., 60:6 (2019), 1075–1082
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https://www.mathnet.ru/eng/smj3155 https://www.mathnet.ru/eng/smj/v60/i6/p1379
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Abstract page: | 249 | Full-text PDF : | 111 | References: | 27 | First page: | 4 |
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