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JOURNALS // Chebyshevskii Sbornik

Chebyshevskii Sb., 2011, Volume 12, Issue 2, Pages 192–203 (Mi cheb91)

Joint universality for zeta-functions of different types
Antanas Laurinčikas, Renata Macaitienė, Darius Šiaučiūnas

References

1. B. Bagchi, The statistical behavior and universality properties of the Riemann zeta-function and other allied Dirichlet series, Ph. D. Thesis, Indian Statistical Institute, Calcuta, 1981
2. B. Bagchi, “A joint universality theorem for Dirichlet $L$-functions”, Math. Z., 181 (1982), 319–334  crossref  mathscinet  zmath  isi
3. P. Deligne, “La conjecture de Weil”, Inst. Hautes $\acute{E}$tudes Sci. Publ. Math., 43 (1974), 273–307  crossref  mathscinet
4. J. Genys, R. Macaitienė, S. Račkauskienė, D. Šiaučiūnas, “A mixed joint universality theorem for zeta-functions”, Mathematical Modelling and Analysis, 15:4 (2010), 431–446  crossref  mathscinet  zmath  isi
5. S. M. Gonek, Analytic properties of zeta and $L$-functions, Ph. D. Thesis, University of Michigan, 1979  mathscinet
6. A. Javtokas, A. Laurinčikas, “The universality of the periodic Hurwitz zeta-function”, Integral Transforms and Special Functions, 17:10 (2006), 711–722  crossref  mathscinet  zmath  isi
7. A. Javtokas, A. Laurinčikas, “A joint universality theorem for periodic Hurwitz zeta-functions”, Bull. Austral. Math. Soc., 78:1 (2008), 13–33  crossref  mathscinet  zmath
8. R. Kačinskaitė, A. Laurinčikas, “The joint distribution of periodic zeta-functions”, Studia Sci. Math. Hungarica, 48:2 (2011), 257–279  mathscinet  isi
9. J. Kaczorowski, “Some remarks on the universality of periodic $L$-functions”, New Directions in Value Distribution Theory of Zeta and $L$-functions, eds. R. Steuding, J. Steuding, Shaker Verlag, Aachen, 2009, 113–120  mathscinet  zmath
10. A. Laurinčikas, Limit Theorems for the Riemann Zeta-Function, Kluwer Academic Publishers, Dordrecht–Boston–London, 1996  mathscinet
11. A. Laurinčikas, “The joint universality for periodic Hurwitz zeta-functions”, Analysis (Munich), 26:3 (2006), 419–428  mathscinet  zmath
12. A. Laurinčikas, “Voronin-type theorem for periodic Hurwitz zeta-functions”, Matem. Sb., 198:2 (2007), 91–102 (in Russian)  mathnet  crossref  zmath
13. A. Laurinčikas, “The joint universality for periodic Hurwitz zeta-functions”, Izv. RAN, Ser. Matem., 72:4 (2008), 121–140 (in Russian)  mathnet  zmath
14. A. Laurinčikas, “The joint universality of Hurwitz zeta-functions”, Šiauliai Math. Semin., 3:11 (2008), 169–187  mathscinet  zmath
15. A. Laurinčikas, “Joint universality of zeta-functions with periodic coefficients”, Izv. RAN, Ser. Matem., 74:3 (2010), 79–102 (in Russian)  mathnet  mathscinet  zmath
16. A. Laurinčikas, R. Garunkštis, The Lerch zeta-function, Kluwer Academic Publishers, Dordrecht–Boston–London, 2002  mathscinet  zmath
17. A. Laurinčikas, R. Macaitienė, “On the joint universality of periodic zeta-functions”, Matem. Zametki, 85:1 (2009), 54–64 (in Russian)  mathnet  crossref  mathscinet  zmath
18. A. Laurinčikas, K. Matsumoto, “The joint universality and the functional independence for Lerch zeta-functions”, Nagoya Math. J., 157 (2000), 211–227  mathscinet  zmath  isi
19. A. Laurinčikas, K. Matsumoto, “The universality of zeta-functions attached to certain cusp forms”, Acta Arith., 98 (2001), 345–359  crossref  mathscinet  zmath  adsnasa  isi
20. A. Laurinčikas, K. Matsumoto, “The joint universality of twisted automorphic $L$-functions”, J. Math. Soc. Jap., 56:3 (2004), 923–939  crossref  mathscinet  zmath
21. A. Laurinčikas, K. Matsumoto, “Joint value distribution theorems on Lerch zeta-functions, III”, Analytic and Probab. Methods in Number Theory, Proc. $4^{\rm th}$ Intern. Conf. in Honour of J. Kubilius, eds. A. Laurinčikas et al., TEV, Vilnius, 2007, 87–98  mathscinet  zmath
22. A. Laurinčikas, K. Matsumoto, J. Steuding, “The universality of $L$-functions associated with new forms”, Izv. RAN, Ser. Matem., 67:1 (2003), 77–90 (in Russian)  mathnet  mathscinet  zmath
23. A. Laurinčikas, S. Skerstonaitė, “A joint universality theorem for periodic Hurwitz zeta-functions, I”, Lith. Math. J., 48:3 (2008), 287–296  mathscinet  isi
24. A. Laurinčikas, S. Skerstonaitė, “Joint universality for periodic Hurwitz zeta-functions, II”, New Dirrections in Value Distribution Theory of Zeta and $L$-functions, eds. R. Steuding, J. Steuding, Shaker Verlag, Aachen, 2009, 161–170  mathscinet
25. A. Laurinčikas, D. Šiaučiūnas, “Remarks on the universality of periodic zeta-function”, Matem. Zametki, 80:4 (2006), 561–568 (in Russian)  mathnet  mathscinet  zmath
26. H. Mishou, “The joint value distribution of the Riemann zeta-function and Hurwitz zeta functions”, Lith. Math. J., 47:1 (2007), 32–47  crossref  mathscinet  zmath  isi
27. T. Nakamura, “The existence and non-existence of joint $t$-universality for Lerch zeta-function”, J. Number Theory, 125:2 (2007), 424–441  crossref  mathscinet  zmath  isi
28. J. Steuding, Value Distribution of $L$-Functions, Lecture Notes Math., 1877, Springer-Verlag, Berlin–Heidelberg–New York, 2007  mathscinet  zmath
29. S. M. Voronin, “Theorem on the “universality” of the Riemann zeta-function”, Izv. Akad. Nauk SSSR, Ser. matem., 39 (1975), 475–486 (in Russian)  mathnet  mathscinet  zmath
30. S. M. Voronin, “The functional independence of Dirichlet $L$-functions”, Acta Arith., 27, 493–503 (in Russian)  mathscinet  zmath


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