Geodesic
Almost periodic functions and property of universality of Dirichlet L-functions
Čebyševskij sbornik, Tome 19 (2018) no. 2, pp. 368-376.

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

The term "universality" for functions was introduced in the early 1970s by E.M. Voronin and the meaning that is embedded in this concept is that a very general class of analytic functions admits approximation by vertical shifts of a given function. In 1975, S.M. Voronin proved the universality property for Riemann zeta-functions, and in 1977 for the Dirichlet L-function. In this paper we propose a proof of the universality property for Dirichlet L-functions that is different from SM's proof. Voronin, based on a rapid approximation in the critical band of Dirichlet L-functions by Dirichlet polynomials.
Keywords: universality property, approximate Dirichlet polynomials, almost periodic functions. 
@article{CHEB_2018_19_2_a25,
     author = {V. N. Kuznetsov and O. A. Matveeva},
     title = {Almost periodic functions and property of universality of {Dirichlet} {L-functions}},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {368--376},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2018_19_2_a25/}
}
TY  - JOUR
AU  - V. N. Kuznetsov
AU  - O. A. Matveeva
TI  - Almost periodic functions and property of universality of Dirichlet L-functions
JO  - Čebyševskij sbornik
PY  - 2018
SP  - 368
EP  - 376
VL  - 19
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2018_19_2_a25/
LA  - ru
ID  - CHEB_2018_19_2_a25
ER  - 
%0 Journal Article
%A V. N. Kuznetsov
%A O. A. Matveeva
%T Almost periodic functions and property of universality of Dirichlet L-functions
%J Čebyševskij sbornik
%D 2018
%P 368-376
%V 19
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2018_19_2_a25/
%G ru
%F CHEB_2018_19_2_a25
V. N. Kuznetsov; O. A. Matveeva. Almost periodic functions and property of universality of Dirichlet L-functions. Čebyševskij sbornik, Tome 19 (2018) no. 2, pp. 368-376. http://geodesic.mathdoc.fr/item/CHEB_2018_19_2_a25/

[1] S. M. Voronin, “Ob universal'nosti dzeta-funkcii Rimana”, Izv. AN SSSR, Serija Matematika, 39:3 (1975), 457–486

[2] S. M. Voronin, “On the functional independence of the Dirichlet L-function”, Acta Arith., 27 (1975), 493–503 | DOI | Zbl

[3] S. M. Voronin, Analytic properties of generating Dirichlet functions of arithmetic objects, Thesis for the academic degree of the Dr. of Science, MIAN SSSR, 1977, 90 pp.

[4] Matveeva O. A., “Approksimacionnye polinomy i povedenie L-funkcij Dirihle v kriticheskoj polose”, Izvestija Sarat. un-ta. Matematika, Mehanika. Informatika, 2013, no. 4-2, 80–84

[5] Kuznetsov V. N., Matveeva O. A., “O granichnom povedenii odnogo klassa rjadov Dirihle s mul'tiplikativnymi kojefficientami”, Chebyshevskij sbornik, 17:3 (2016), 115–124 | DOI

[6] Kuznetsov V. N., Matveeva O. A., “Approksimacionnyj podhod v nekotoryh zadachah teorii rjadov Dirihle s mul'tiplikativnymi kojefficientami”, Chebyshevskij sbornik, 17:4 (2016), 124–131 | DOI | MR | Zbl

[7] Kuznetsov V. N., Matveeva O. A., “Approximation Dirichlet polynomials and some properties of Dirichlet L-functions”, Chebyshevskij sbornik, 18:4 (2017), 296–304 | MR

[8] H. Mishou, “The joint distribution of the Riemann zeta-function and Hurwitz zeta-function”, Lith. Math. J., 47:1 (2007), 32–47 | DOI | MR | Zbl

[9] A. Laurincikas, “The universality of zeta-functions”, Acta Appe. Math., 78:1–3 (2003), 251–271 | DOI | MR | Zbl

[10] R. Kacinskait, A. Laurincikas, “The joint distribution of periodic zeta-function”, Studia Sci. Math. Hungar., 48:2 (2011), 257–279 | MR | Zbl

[11] E. Buivydas, A. Laurincikas, “A discrete version of the Mishou theorem”, Ramanujan J., 38:2 (2015), 331–347 | DOI | MR | Zbl

[12] A. Laurincikas, R. Garunkstis, The Lerch Zeta-function, Kluwer Acad. Publ., Dordrecht, 2002 | MR | Zbl

[13] B. P. Demidovich, Lekcii po matematicheskoj teorii ustojchivosti, MSU publ., M., 1998, 480 pp.

[14] B. Ja. Levin, Raspredlenie kornej celyh funkcij, Izd-vo tehniko-teoreticheskoj literatury, M., 1956, 632 pp.

[15] Titchmarsh E. K., Teorija dzeta-funkcii Rimana, IL, M., 1953, 407 pp.