On the Mishou Theorem with an Algebraic Parameter
- Authors: Laurinčikas A.1
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Affiliations:
- Institute of Mathematics
- Issue: Vol 60, No 6 (2019)
- Pages: 1075-1082
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172766
- DOI: https://doi.org/10.1134/S0037446619060144
- ID: 172766
Cite item
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.
About the authors
A. Laurinčikas
Institute of Mathematics
Author for correspondence.
Email: antanas.laurincikas@mif.vu.lt
Lithuania, Vilnius