Discrete limit theorems for general Dirichlet series. III

A. Laurinčikas; R. Macaitienė

Open Mathematics (2004)

  • Volume: 2, Issue: 3, page 339-361
  • ISSN: 2391-5455

Abstract

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Here we prove a limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for a general Dirichlet series. The explicit form of the limit measure in this theorem is given.

How to cite

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A. Laurinčikas, and R. Macaitienė. "Discrete limit theorems for general Dirichlet series. III." Open Mathematics 2.3 (2004): 339-361. <http://eudml.org/doc/268884>.

@article{A2004,
abstract = {Here we prove a limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for a general Dirichlet series. The explicit form of the limit measure in this theorem is given.},
author = {A. Laurinčikas, R. Macaitienė},
journal = {Open Mathematics},
keywords = {11M41; 30B50; 60B10},
language = {eng},
number = {3},
pages = {339-361},
title = {Discrete limit theorems for general Dirichlet series. III},
url = {http://eudml.org/doc/268884},
volume = {2},
year = {2004},
}

TY - JOUR
AU - A. Laurinčikas
AU - R. Macaitienė
TI - Discrete limit theorems for general Dirichlet series. III
JO - Open Mathematics
PY - 2004
VL - 2
IS - 3
SP - 339
EP - 361
AB - Here we prove a limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for a general Dirichlet series. The explicit form of the limit measure in this theorem is given.
LA - eng
KW - 11M41; 30B50; 60B10
UR - http://eudml.org/doc/268884
ER -

References

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  1. [1] P. Billingsley:Convergence of Probability Measures, Wiley, New York, 1968. 
  2. [2] H. Bohr and B. Jessen: “Über die Werverteilung der Riemannschen Zeta function”. Erste Mitteilung.Acta Math., Vol. 54, (1930), pp. 1–35. Zbl56.0287.01
  3. [3] H. Bohr and B. Jessen: “Über die Werverteilung der Riemannschen Zeta function”. Zweite Mitteilung,Acta Math., Vol. 54, (1932), pp. 1–55. Zbl58.0321.02
  4. [4] J. Genys and A. Laurinčikas: “Value distribution of general Dirichlet series IV”,Lith. Math. J., Vol. 43, No. 3, (2003), pp. 342–358;Lith. Math. J., Vol. 43, No. 3, (2003), pp. 281–294 (in Russian). http://dx.doi.org/10.1023/A:1026189318741 
  5. [5] A. Laurinčikas:Limit Theorems for the Riemann Zeta-Function, Kluwer, Dordrecht, 1996. 
  6. [6] A. Laurinčikas: “Value distribution of general Dirichlet series”, In: B. Grigelionis et al. (Eds.):Probab. Theory and Math. Statistics; Proceedings of the seventh Vilnius, TEV, Vilnius, (1999), pp. 405–414. Zbl1095.11503
  7. [7] A. Laurinčikas: “Value distribution of general Dirichlet series. II”,Lith. Math. J., Vol. 41, No. 4, (2001), pp. 351–360. http://dx.doi.org/10.1023/A:1013860521038 
  8. [8] A. Laurinčikas: “Limit theorems for general Dirichlet series”,Theory Stoch. Proc., Vol. 8, No. 24, (2002), pp. 256–268. 
  9. [9] A. Laurinčikas, W. Schwarz and J. Steuding: “Value distribution of general Dirichelet series. III”, In: A. Dubickas et al. (Eds.):Analytic and Probab. Methods in Number Theory. Proc. The Third Palanga Conf., TEV, Vilnius, (2002), pp. 137–156. Zbl1195.11118
  10. [10] A. Laurinčikas and R. Macaitienė: “Discrete limit theorems for general Dirichlet series. I,”Chebyshevski sbornik, Vol. 4, No. 3, (2003), pp. 156–170. Zbl1105.11030
  11. [11] R. Macaitienė: “Discrete limit theorems for general Dirichlet polynomials”,Lith. Math. J., Vol. 42 (spec. issue), (2002), pp. 705–709. 
  12. [12] R. Macaitienė: “Discrete limit theorems for general Dirichlet series. II”,Lith. Math. J., (to appear). Zbl1084.60016
  13. [13] H.L. Montgomery:Topics in multiplicative number theory, Springer, Berlin, 1971. Zbl0216.03501
  14. [14] E.M. Nikishin: “Dirichlet series with independent exponents and certain of their applications”,Matem.sb, Vol. 96, No. 1, (1975), pp. 3–40 (in Russian). 
  15. [15] Y.G. Sinai:Introduction to Ergodic Theory, Princeton Univ. Press, 1976. 
  16. [16] A.A. Tempelman:Ergodic Theorems on Groups, Mokslas, Vilnius, 1986. 

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