右半平面无限级随机Dirichlet级数值的分布

Abstract

Abstract:

The emphasis in this paper is mainly on the distribution of values of the infinite order random Dirichlet series on the right half-plane. Firstly, the theorem of the growth and the distribution of value of the Dirichlet series on the right half-plane are proved under some weak conditions of the coefficient. Secondly, the random Dirichlet series the norms of whose coefficients are pairwise NQD sequences are investigated and some better results similar to the case of independent random sequences are obtained. Under some conditions, the random series X_ne^-λ_ns and the series σ_ne^-λ_ns a.s. have the same abscissa of convergence, the order of growth, the type function on the right half-plane.

Key words: Random Dirichlet series, Growth, Distribution of value, Pairwise NQD sequence, Type function

CLC Number:

O211.5

Wang Zhigang, Tian Fanji. The Distribution of Values of the Infinite Order Random Dirichlet Series on the Right Half-Plane[J].Acta mathematica scientia,Series A, 2015, 35(2): 245-255.

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The Distribution of Values of the Infinite Order Random Dirichlet Series on the Right Half-Plane

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