Discrete Universality of $L$-Functions for New Forms
Matematičeskie zametki, Tome 78 (2005) no. 4, pp. 595-603.

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

A Voronin-type discrete universality theorem for the $L$-functions of new forms is proved.
@article{MZM_2005_78_4_a8,
     author = {A. P. Laurincikas and K. Matsumoto and J. Steuding},
     title = {Discrete {Universality} of $L${-Functions} for {New} {Forms}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {595--603},
     publisher = {mathdoc},
     volume = {78},
     number = {4},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_78_4_a8/}
}
TY  - JOUR
AU  - A. P. Laurincikas
AU  - K. Matsumoto
AU  - J. Steuding
TI  - Discrete Universality of $L$-Functions for New Forms
JO  - Matematičeskie zametki
PY  - 2005
SP  - 595
EP  - 603
VL  - 78
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2005_78_4_a8/
LA  - ru
ID  - MZM_2005_78_4_a8
ER  - 
%0 Journal Article
%A A. P. Laurincikas
%A K. Matsumoto
%A J. Steuding
%T Discrete Universality of $L$-Functions for New Forms
%J Matematičeskie zametki
%D 2005
%P 595-603
%V 78
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2005_78_4_a8/
%G ru
%F MZM_2005_78_4_a8
A. P. Laurincikas; K. Matsumoto; J. Steuding. Discrete Universality of $L$-Functions for New Forms. Matematičeskie zametki, Tome 78 (2005) no. 4, pp. 595-603. http://geodesic.mathdoc.fr/item/MZM_2005_78_4_a8/

[1] Voronin S. M., “Teorema ob “universalnosti” dzeta-funktsii Rimana”, Izv. AN SSSR. Ser. matem., 39:3 (1975), 475–486 | MR | Zbl

[2] Voronin S. M., “Teorema o raspredelenii znachenii dzeta-funktsii Rimana”, Dokl. AN SSSR, 221:4 (1975), 771 | MR | Zbl

[3] Voronin S. M., Issledovanie povedeniya dzeta-funktsii Rimana, Diss. ... k. f.-m. n., Matem. institut AN SSSR, M., 1972 | Zbl

[4] Voronin S. M., Analiticheskie svoistva proizvodyaschikh funktsii Dirikhle arifmeticheskikh ob'ektov, Diss. ... d. f.-m. n., Matem. institut AN SSSR, M., 1977

[5] Voronin S. M., “Analiticheskie svoistva proizvodyaschikh funktsii Dirikhle arifmeticheskikh ob'ektov”, Matem. zametki, 24:6 (1978), 879–884 | MR | Zbl

[6] Voronin S. M., Karatsuba A. A., Dzeta-funktsiya Rimana, Fizmatlit, M., 1994

[7] Laurinčikas A., Limit Theorems for the Riemann Zeta-function, Kluwer Acad. Publ., Dordrecht–Boston–London, 1996 | MR

[8] Gonek S. M., Analytic Properties of Zeta and $L$-functions, Ph. D. Thesis, University of Michigan, Michigan, 1979

[9] Reich A., “Universelle Wertverteilung von Eulerprodukten”, Nachr. Akad. Wiss. Göttingen. Math.-Phys. Kl. II, 1977, no. 1, 1–17 | Zbl

[10] Reich A., “Zur Universalität und Hypertranszendenz der Dedekindschen Zetafunktion”, Abh. Braunschweig. Wiss. Ges., 33 (1982), 187–203

[11] 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

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

[13] Laurinčikas A., “Distribution des valeurs de certaines séries de Dirichlet”, C. R. Acad. Sci. Paris Sér. A, 289 (1979), 43–45 | Zbl

[14] Laurinchikas A., “Universalnost dzeta-funktsii Lerkha”, Litovskii matem. sb., 37:2 (1997), 367–375 | Zbl

[15] Laurinčikas A., “On the Matsumoto zeta-function”, Acta Arith., 84 (1988), 1–16

[16] Laurinčikas A., “The universality of zeta-functions”, Acta Appl. Math., 78 (2003), 251–271 | DOI | Zbl

[17] Laurinčikas A., On the derivatives of zeta-functions of certain cusp forms, Preprint 2004-06, Department Math. and Inform., Vilnius University, Vilnius, 2004

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

[19] Laurinčikas A., Matsumoto K., “The universality of zeta-functions attached to certain cusp-forms”, Acta Arith., 98 (2001), 345–359 | DOI | Zbl

[20] Laurichikas A., Matsumoto K., Steuding I., “Universalnost $L$-funktsii svyazannykh s novymi formami”, Izv. RAN. Ser. matem., 67:1 (2003), 83–98

[21] Matsumoto K., “The mean values and the universality of Rankin–Selberg $L$-functions”, Number Theory, Proceedings of the Turku Symposium on number theory in memory Kustaa Inkeri (1999), eds. M. Jutila, T. Metsänkylä, Walter de Gruyter, Berlin–New York, 2001, 201–221

[22] Steuding J., “Upper bounds for the density of universality”, Acta Arith., 107 (2003), 195–202 | DOI | Zbl

[23] Steuding J., “On the universality for functions in the Selberg class”, Paper \char242 28, Proc. Session in Analytic Number Theory and Diophantine Equations (January–June 2002), Bonner Math. Schriften, 360, eds. D. R. Heath-Brown, B. Z. Moroz, MPI Bonn, Bonn, 2003

[24] Mishou H., “The universality theorem for $L$-functions associated with ideal class characters”, Acta Arith., 98 (2001), 395–410 | DOI | Zbl

[25] Mishou H., “The universality theorem for Hecke $L$-functions”, Acta Arith., 110 (2003), 45–71 | DOI | Zbl

[26] Bauer H., “The value distribution of Artin $L$-series and zeros of zeta-functions”, J. Number Theory, 98 (2003), 254–279 | DOI | Zbl

[27] Garunkštis R., “The effective universality theorem for the Riemann zeta-function”, Proc. Session in Analytic Number Theory and Diophantine Equations (January–June 2002), Bonner Math. Schriften, 360, eds. D. R. Heath-Brown, B. Z. Moroz, MPI Bonn, Bonn, 2003, 1–21

[28] Laurinčikas A., Schwarz W., Steuding J., “The universality of general Dirichlet series”, Analysis, 23 (2003), 13–26 | Zbl

[29] Breuil C., Conrad B., Diamond F., Taylor R., “On the modularity of elliptic curves over $\mathbb Q$: wild $3$-adic exercises”, J. Amer. Math. Soc., 14 (2001), 843–939 | DOI | Zbl

[30] Kachinskaite R., “Diskretnaya predelnaya teorema dlya Matsumoto dzeta-funktsii v prostranstve meromorfnykh funktsii”, Litovskii matem. sb., 42:1 (2002), 46–67

[31] Matsumoto K., “Value-distribution of zeta-functions”, Lecture Notes in Math., 1434, 1990, 178–187 | Zbl

[32] Matsumoto K., “A probabilistic study on the value distribution of Dirichlet series attached to certain cusp forms”, Nagoya Math. J., 116 (1989), 123–138 | Zbl

[33] Billingsley P., Convergence of Probability Measures, John Wiley, New York, 1967

[34] Walsh J. L., Interpolation and Approximation by Rational Functions in the Complex Domain, Amer. Math. Soc. Colloq. Publ., 20, Amer. Math. Soc., Providence, RI, 1960 | Zbl