On a Dirichlet series connected to a periodic Hurwitz zeta-function with transcendental and rational parameter
Abstract
In the paper, we construct an absolutely convergent Dirichlet series which in the mean is close to the periodic Hurwitz zeta-function, and has the universality property on the approximation of a wide class of analytic functions.
Keywords:
Haar measure, periodic Hurwitz zeta-function, space of analytic functions, universality, weak convergenceHow to Cite
Share
License
Copyright (c) 2023 The Author(s). Published by Vilnius Gediminas Technical University.
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
P. Billingsley. Convergence of Probability Measures. Wiley, New York, 1968.
A. Javtokas and A. Laurinčikas. On the periodic Hurwitz zeta-function. HardyRamanujan Journal, 29:18–36, 2006. https://doi.org/10.46298/hrj.2006.154"> https://doi.org/10.46298/hrj.2006.154
A. Javtokas and A. Laurinčikas. Universality of the periodic Hurwitz zetafunction. Integral Transforms and Special Functions, 17(10):711–722, 2006. https://doi.org/10.1080/10652460600856484"> https://doi.org/10.1080/10652460600856484
A. Laurinčikas, R. Macaitienė, D. Mochov and D. Šiaučiūnas. Universality of the periodic Hurwitz zeta-function with rational parameter. Siberian Mathematical Journal, 59(5):894–900, 2018. https://doi.org/10.1134/S0037446618050130"> https://doi.org/10.1134/S0037446618050130
S.N. Mergelyan. Uniform approximations to functions of complex variable. Uspekhi Mat. Nauk, 7(2):31–122, 1952. (in Russian).
S.M. Voronin. Theorem on the “universality” of the Riemann zetafunction. Mathematics of the USSR-Izvestiya, Ser. Matem., 9(3):475–486, 1975. https://doi.org/10.1070/IM1975v009n03ABEH001485"> https://doi.org/10.1070/IM1975v009n03ABEH001485 (in Russian).
View article in other formats
CrossMark check
Published
Issue
Section
Copyright
Copyright (c) 2023 The Author(s). Published by Vilnius Gediminas Technical University.
License
This work is licensed under a Creative Commons Attribution 4.0 International License.