On limit distribution of the Hurwitz zeta-function

• Autorzy: Antanas Laurinčikas
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Characteristic transform; Hurwitz zeta-function; Probability measure; Weak convergence

Kategorie tematyczne

• 11M35: Hurwitz and Lerch zeta functions

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 4
• Strony: 786-794

Daty

wydano

2010-08-01

online

2010-07-24

Twórcy

autor

Antanas Laurinčikas

• Department of Matematics and Informatics, Vilnius University, Vilnius, Lithuania

Bibliografia

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

Identyfikatory

DOI

10.2478/s11533-010-0043-2