Geodesic
On joint universality of Dirichlet $L$-functions
Čebyševskij sbornik, Tome 12 (2011) no. 1, pp. 124-139.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper, we present a probabilistic proof of the Voronin theorem on joint un universality of Dirichlet $L$-functions, and prove the universality for some composite functions. 
@article{CHEB_2011_12_1_a9,
     author = {A. Laurin\v{c}ikas},
     title = {On joint universality of {Dirichlet} $L$-functions},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {124--139},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2011_12_1_a9/}
}
TY  - JOUR
AU  - A. Laurinčikas
TI  - On joint universality of Dirichlet $L$-functions
JO  - Čebyševskij sbornik
PY  - 2011
SP  - 124
EP  - 139
VL  - 12
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2011_12_1_a9/
LA  - en
ID  - CHEB_2011_12_1_a9
ER  - 
%0 Journal Article
%A A. Laurinčikas
%T On joint universality of Dirichlet $L$-functions
%J Čebyševskij sbornik
%D 2011
%P 124-139
%V 12
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2011_12_1_a9/
%G en
%F CHEB_2011_12_1_a9
A. Laurinčikas. On joint universality of Dirichlet $L$-functions. Čebyševskij sbornik, Tome 12 (2011) no. 1, pp. 124-139. http://geodesic.mathdoc.fr/item/CHEB_2011_12_1_a9/

[1] Bagchi B., The statistical behaviour and universality properties of the Riemann zeta-function and other allied Dirichlet series, Ph. D. Thesis, Indian Statistical Institute, Calcutta, 1981

[2] Bagchi B., “A joint universality theorem for Dirichlet $L$-functions”, Math. Z., 181 (1982), 319–334 | DOI | MR | Zbl

[3] Billingsley P., Convergence of Probability Measures, Willey, New York, 1968 | MR | Zbl

[4] Gonek S. M., Analytic properties of zeta and $L$-functions, Ph. D. Thesis, University of Michigan, 1979 | MR

[5] Karatsuba A. A., Voronin S. M., The Riemann Zeta-Function, de Gruyter, New York, 1992 | MR | Zbl

[6] Lang S., Algebra, Addison-Wesley, Reading, Mass., 1967 | MR | Zbl

[7] Laurinčikas A., Limit Theorems for the Riemann Zeta-Function, Kluwer Academic Publishers, Dordrecht–Boston–London, 1996 | MR

[8] Laurinčikas A., Matsumoto K., “The joint universality and the functional independence for Lerch zeta-functions”, Nagoya Math. J., 157 (2000), 211–227 | MR | Zbl

[9] Laurinčikas A., Matsumoto K., “The joint universality of zeta-functions attached to certain cusp forms”, Fiz. Mat. Fak. Moksl. Semin. Darb., 5 (2002), 58–75 | MR | Zbl

[10] Mergelyan S. N., “Uniform approximations to functions of complex variable”, Usp. Mat. Nauk (N.S.), 7 (1952), 31–122 (in Russian) | MR | Zbl

[11] Steuding J., “Value Distribution of $L$-Functions”, Lecture Notes Math., 1877, Springer-Verlag, Berlin–Heidelberg–New York, 2007 | MR | Zbl

[12] Titchmarsh E. C., The Theory of Functions, Oxford University Press, Oxford, 1939

[13] Voronin S. M., “Theorem on the “universality” of the Riemann zeta-function”, Izv. Akad. Nauk SSSR, Ser. matem., 39 (1975), 475–486 (in Russian) | MR | Zbl

[14] Voronin S. M., “The functional independence of Dirichlet $L$-functions”, Acta Arith., 27 (1975), 493–503 (in Russian) | MR | Zbl

[15] Walsh J. L., Interpolation and Approximation by Rational Functions in the Complex Domain, Amer. Math. Soc. Coll. Publ., 20, 1960 | MR | Zbl