Abstract
In this paper we prove a generalized version of a joint discrete universality theorem on the approximation of a collection of analytic functions by discrete shifts of Dirichlet L-functions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. Bagchi, The statistical behaviour and universality properties of the Riemann zeta-function and other allied Dirichlet series, Ph. D. Thesis, Indian Stat. Institute, Calcutta, 1981.
Bagchi B.: A joint universality theorem for Dirichlet L-functions, Math. Z. 181, 319–334 (1982)
P. Billingsley, Convergence of Probability Measures, Willey, New York, 1968.
G.E. Bredon, Topology and Geometry, Graduate Texts in Mathematics 139, Springer, New York, 1993.
S.M. Gonek, Analytic properties of zeta and L-functions, Ph. D. Thesis, University of Michigan, 1979.
H. Heyer, Probability Measures on Locally Compact Groups, Springer-Verlag, Berlin, Heidelberg, New York, 1977.
A.A. Karatsuba and S.M. Voronin, The Riemann Zeta-Function, Walter de Gruyter, 1992.
A. Laurinčikas, Joint universality of zeta-functions with periodic coefficients, Izv. RAN, Ser. Mat. 74 (2010), 79–102 (In Russian) ≡ Izv. Math. 74 (2010), 515–539.
Laurinčikas A.: On joint universality of Dirichlet L-functions, Chebysh. Sbornik 12(No. 1), 124–139 (2011)
A. Laurinčikas and R. Garunkštis, The Lerch Zeta-Function, Kluwer, Dordrecht, 2002.
K. Matsumoto, A survey on the theory of universality for zeta and L-functions, (to appear).
S.N. Mergelyan, Uniform approximations to functions of a complex variable, Uspekhi Matem. Nauk 7(2) (1952), 31–122 (In Russian) ≡ Amer. Math. Soc. Transl. 101 (1954).
H.L. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes Math. 227, Springer, Berlin, 1971.
J. Steuding, Value-Distribution of Dirichlet L-Functions, Lecture Notes Math. 1877, Springer, Berlin, 2007.
S.M. Voronin, Theorem on the “universality” of the Riemann zeta-function, Izv. AN SSSR, Ser. Mat. 39 (1975), 475–486 (In Russian) ≡ Math. USSR Izv. 9 (1975), 443–453.
S.M. Voronin, On the functional independence of Dirichlet L-functions, Acta Arith. 27 (1975), 493–503 (In Russian).
S.M. Voronin, Analytic properties of Dirichlet generating functions of arithmetic objects, Thesis doktora fiz.-mat. nauk, Steklov Math. Inst. Moscow, 1977 (In Russian).
S.M. Voronin, Izbrannye trudy, Matematika, A.A Karatsuba (Ed), Izd. MGTU im. Baumana, Moskva, 2006.
J.L. Walsh, Interpolation and Approximation by Rational Functions in the Complex Domain, Amer. Math. Soc., Providence, RI, 1965.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dubickas, A., Laurinčikas, A. Joint discrete universality of Dirichlet L-functions. Arch. Math. 104, 25–35 (2015). https://doi.org/10.1007/s00013-014-0721-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-014-0721-6