Abstract
Considering periodic \( \zeta \)-functions and periodic Hurwitz \( \zeta \)-functions, we obtain joint universality for approximation to a collection of analytic functions by generalized shifts of the \( \zeta \)-functions.
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References
Voronin S. M., “Theorem on the ‘universality’ of the Riemann zeta-function,” Math. USSR-Izv., vol. 9, no. 3, 443–453 (1975).
Matsumoto K., “A survey of the theory of universality for zeta and \( L \)-functions,” in: Number Theory: Plowing and Staring Through High Wave Forms, Ser. Number Theory and Its Appl. V. 11. Proc. 7\( th \) China–Japan Seminar (Fukuoka, 2013), World Sci., New Jersey, London, Singapore, Beijing, Shanghai, Hong Kong, Taipei, and Chennai (2015), 95–144.
Laurinčikas A.,Limit Theorems for the Riemann Zeta-Function, Kluwer, Dordrecht, Boston, and London (1996).
Laurinčikas A. and Garunkštis R.,The Lerch Zeta-Function, Kluwer, Dordrecht, Boston, and London (2002).
Steuding J.,Value-Distribution of \( L \)-Functions, Springer, Berlin, Heidelberg, and New York (2007) (Lecture Notes Math.; Vol. 1877).
Bagchi B.,The Statistical Behaviour and Universality Property of the Riemann Zeta-Function and Other Allied Dirichlet Series. PhD Dissertation, Indian Statistical Inst., Calcutta (1981).
Gonek S. M.,Analytic Properties of Zeta- and \( L \)-Functions. PhD Dissertation, University of Michigan, Ann Arbor (1979).
Bagchi B., “Recurrence in topological dynamics and the Riemann hypothesis,” Acta Math. Hung., vol. 50, 227–240 (1987).
Kačinskaite R. and Laurinčikas A., “The joint distribution of periodic zeta-functions,” Stud. Sci. Math. Hung., vol. 48, 257–279 (2011).
Laurinčikas A., “Joint universality of zeta-functions with periodic coefficients,” Izv. Math., vol. 74, no. 3, 315–539 (2010).
Laurinčikas A., “Joint discrete universality for periodic zeta-functions,” Quaest. Math., vol. 42, 687–699 (2019).
Karatsuba A. A. and Voronin S. M.,The Riemann Zeta-Function, De Gruyter, Berlin (1992).
Billingsley P.,Convergence of Probability Measures, Wiley, New York (1975).
Mergelyan S. N., “Uniform approximations of functions of a complex variable,” Uspekhi Mat. Nauk, vol. 7, no. 2, 31–122 (1952).
Funding
The research was funded by the European Social Fund according to the activity “Improvement of Researchers’ Qualification by Implementing World-Class R&D Projects” (Grant 09.3.3–LMT–K–712–01–0037).
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Laurinčikas, A. Joint Universality of Zeta Functions with Periodic Coefficients. II. Sib Math J 61, 848–858 (2020). https://doi.org/10.1134/S0037446620050080
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DOI: https://doi.org/10.1134/S0037446620050080