On limit distribution of the Hurwitz zeta-function

Antanas Laurinčikas

Open Mathematics (2010)

  • Volume: 8, Issue: 4, page 786-794
  • ISSN: 2391-5455

Abstract

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The distribution of the vector (|ζ(s, α)|; ζ(s, α)), where ζ(s, α) is the Hurwitz zeta-function with transcendental parameter α, is considered and a probabilistic limit theorem is obtained. Also, the dependence between |ζ(s, α)| and ζ(s, α) in terms of m-characteristic transforms is discussed.

How to cite

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Antanas Laurinčikas. "On limit distribution of the Hurwitz zeta-function." Open Mathematics 8.4 (2010): 786-794. <http://eudml.org/doc/269104>.

@article{AntanasLaurinčikas2010,
abstract = {The distribution of the vector (|ζ(s, α)|; ζ(s, α)), where ζ(s, α) is the Hurwitz zeta-function with transcendental parameter α, is considered and a probabilistic limit theorem is obtained. Also, the dependence between |ζ(s, α)| and ζ(s, α) in terms of m-characteristic transforms is discussed.},
author = {Antanas Laurinčikas},
journal = {Open Mathematics},
keywords = {Characteristic transform; Hurwitz zeta-function; Probability measure; Weak convergence; characteristic transform; probability measure; weak convergence},
language = {eng},
number = {4},
pages = {786-794},
title = {On limit distribution of the Hurwitz zeta-function},
url = {http://eudml.org/doc/269104},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Antanas Laurinčikas
TI - On limit distribution of the Hurwitz zeta-function
JO - Open Mathematics
PY - 2010
VL - 8
IS - 4
SP - 786
EP - 794
AB - The distribution of the vector (|ζ(s, α)|; ζ(s, α)), where ζ(s, α) is the Hurwitz zeta-function with transcendental parameter α, is considered and a probabilistic limit theorem is obtained. Also, the dependence between |ζ(s, α)| and ζ(s, α) in terms of m-characteristic transforms is discussed.
LA - eng
KW - Characteristic transform; Hurwitz zeta-function; Probability measure; Weak convergence; characteristic transform; probability measure; weak convergence
UR - http://eudml.org/doc/269104
ER -

References

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  1. [1] 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 
  2. [2] Billingsley P., Convergence of Probability Measures, Wiley, New York, 1968 Zbl0172.21201
  3. [3] Genys J., Laurinčikas A., Weighted limit theorems for general Dirichlet series, Unif. Distrib. Theory, 2007, 2(2), 49–66 Zbl1174.11070
  4. [4] Laurinčikas A., Distribution of values of complex-valued functions, Litovsk. Mat. Sb., 1975, 15(2), 25–39, (in Russian) Zbl0311.10047
  5. [5] Laurinčikas A., Limit Theorems for the Riemann Zeta-Function, Kluwer Academic Publishers, Dordrecht, 1996 
  6. [6] Laurinčikas A., Limit theorems for general Dirichlet series, Theory Stoch. Process., 2002, 8(3–4), 256-268 
  7. [7] Laurinčikas A., Remarks on characteristic transforms of probability measures, Šiauliai Math. Semin., 2007, 2(10), 43–52 Zbl1136.60310
  8. [8] Laurinčikas A., Garunkštis R., The Lerch Zeta-Function, Kluwer, Dordrecht, 2002 Zbl1028.11052
  9. [9] Laurinčikas A., Macaitienė R., The characteristic transforms on ℝ×ℂ, Integral Transforms Spec. Funct., 2008, 19(1–2), 11–22 
  10. [10] Matsumoto K., Probabilistic value-distribution theory of zeta-functions, Sugaku Expositions, 2004, 17(1), 51–71 Zbl1246.11142
  11. [11] Steuding J., Value-Distribution of L-Functions, Lecture Notes in Mathematics, 1877, Springer, Berlin, 2007 Zbl1130.11044

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