MODIFICATION OF THE MISHOU THEOREM
https://doi.org/10.22405/2226-8383-2016-17-3-135-147
Abstract
The Mishou theorem asserts that a pair of analytic functions from a wide class can be approximated by shifts of the Riemann zeta and Hurwitz zeta-functions \((\zeta(s+i\tau), \zeta(s+i\tau, \alpha))\) with transcendental \(\alpha\), \(\tau\in\mathbb{R}\), and that the set of such \(\tau\) has a positive lower density. In the paper, we prove that the above set has a positive density for all but at most countably many \(\varepsilon>0\), where \(\varepsilon\) is the accuracy of approximation. We also obtain similar results for composite functions \(F(\zeta(s),\zeta(s,\alpha))\) for some classes of operator \(F\).
About the Authors
A. Laurinčikas
Vilnius University
Russian Federation
Full member of the AS in Lithuania, doctor of physical and mathematical sciences, professor, head of probability theory’s and number theory’s chair
Russian Federation
Full member of the AS in Lithuania, doctor of physical and mathematical sciences, professor, head of probability theory’s and number theory’s chair
L. Meška
Vilnius University
Russian Federation
doctoral student of the Faculty of Mathematics and Informatics
Russian Federation
doctoral student of the Faculty of Mathematics and Informatics
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Review
For citations:
Laurinčikas A., Meška L. MODIFICATION OF THE MISHOU THEOREM. Chebyshevskii Sbornik. 2016;17(3):135-147. (In Russ.) https://doi.org/10.22405/2226-8383-2016-17-3-135-147
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