Discrete universality of absolutely convergent Dirichlet series
Abstract
In the paper, an universality theorem of discrete type on the approximation of analytic functions by shifts of a special absolutely convergent Dirichlet series is obtained. These series is close in a certain sense to the periodic zeta-function and depends on a parameter.
Keyword : limit theorem, periodic zeta-function, universality, weak convergence
How to Cite
Jasas, M., Laurinčikas, A., Stoncelis, M., & Šiaučiūnas, D. (2022). Discrete universality of absolutely convergent Dirichlet series. Mathematical Modelling and Analysis, 27(1), 78–87. https://doi.org/10.3846/mma.2022.15069
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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A. Laurinčikas. Limit Theorems for the Riemann Zeta-Function. Kluwer, Dordrecht, 1996. https://doi.org/10.1007/978-94-017-2091-5
A. Laurinčikas. The joint discrete universality of periodic zeta-functions. In J. Sander, J. Steuding and R. Steuding(Eds.), From Arithmetic to Zeta-Functions, Number Theory in Memory of Wolfgang Schwarz, pp. 231–246. Springer, 2016. https://doi.org/10.1007/978-3-319-28203-9_15
R. Macaitienė, M. Stoncelis and D. Šiaučiūnas. A weighted discrete universality theorem for periodic zeta-functions. In A. Dubickas, A. Laurinčikas, E. Manstavičius and G. Stepanauskas(Eds.), Anal. Probab. Methods Number Theory, Proc. 6th Int. Conf., Palanga, Lithuania, 11–17 September 2016, pp. 97–107, Vilnius, 2017. VU Leidykla.
R. Macaitienė, M. Stoncelis and D. Šiaučiūnas. A weighted discrete universality theorem for periodic zeta-functions. II. Mathematical Modelling and Analysis, 22(6):750–762, 2017. https://doi.org/10.3846/13926292.2017.1365779
K. Matsumoto. A survey on the theory of universality for zeta and L-functions. In M. Kaneko, S. Kanemitsu and J. Liu(Eds.), Number Theory: Plowing and Starring Through High Wawe Forms, Proc. 7th China-Japan Semin. (Fukuoka 2013), volume 11 of Number Theory and its Applications, pp. 95–144, New Jersey, London, Singapore, Beijing, Shanghai, Hong Kong, Taipei, Chennai, 2015. World Scientific Publishing Co. https://doi.org/10.1142/9789814644938_0004
S.N. Mergelyan. Uniform approximations to functions of complex variable. Usp. Mat. Nauk., 7(2):31–122, 1952 (in Russian).
H.L. Montgomery. Topics in Multiplicative Number Theory. Lecture Notes Math. Vol. 227, Springer-Verlag, Berlin, 1971. https://doi.org/10.1007/BFb0060851