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JOURNALS // Matematicheskie Zametki

Mat. Zametki, 2005, Volume 78, Issue 4, Pages 595–603 (Mi mzm2617)

Discrete Universality of $L$-Functions for New Forms
A. P. Laurincikas, K. Matsumoto, J. Steuding

References

1. Voronin S. M., “Teorema ob “universalnosti” dzeta-funktsii Rimana”, Izv. AN SSSR. Ser. matem., 39:3 (1975), 475–486  mathnet  mathscinet  zmath
2. Voronin S. M., “Teorema o raspredelenii znachenii dzeta-funktsii Rimana”, Dokl. AN SSSR, 221:4 (1975), 771  mathnet  mathscinet  zmath
3. Voronin S. M., Issledovanie povedeniya dzeta-funktsii Rimana, Diss. … k. f.-m. n., Matem. institut AN SSSR, M., 1972  zmath
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  mathnet  mathscinet  zmath
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  mathscinet
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  zmath
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  crossref  zmath
13. Laurinčikas A., “Distribution des valeurs de certaines séries de Dirichlet”, C. R. Acad. Sci. Paris Sér. A, 289 (1979), 43–45  zmath
14. Laurinchikas A., “Universalnost dzeta-funktsii Lerkha”, Litovskii matem. sb., 37:2 (1997), 367–375  zmath
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  crossref  zmath
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  zmath
19. Laurinčikas A., Matsumoto K., “The universality of zeta-functions attached to certain cusp-forms”, Acta Arith., 98 (2001), 345–359  crossref  zmath
20. Laurichikas A., Matsumoto K., Steuding I., “Universalnost $L$-funktsii svyazannykh s novymi formami”, Izv. RAN. Ser. matem., 67:1 (2003), 83–98  mathnet
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  crossref  zmath
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  crossref  zmath
25. Mishou H., “The universality theorem for Hecke $L$-functions”, Acta Arith., 110 (2003), 45–71  crossref  zmath
26. Bauer H., “The value distribution of Artin $L$-series and zeros of zeta-functions”, J. Number Theory, 98 (2003), 254–279  crossref  zmath
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  zmath
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  crossref  zmath
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  zmath
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  zmath
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  zmath


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