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.
Keyword : Haar measure, periodic Hurwitz zeta-function, space of analytic functions, universality, weak convergence
How to Cite
Balčiūnas, A., Laurinčikas, A., & Stoncelis, M. (2023). On a Dirichlet series connected to a periodic Hurwitz zeta-function with transcendental and rational parameter. Mathematical Modelling and Analysis, 28(1), 91–101. https://doi.org/10.3846/mma.2023.17222
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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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
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
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
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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 (in Russian).
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
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
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
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 (in Russian).