半平面上无限级Dirichlet级数与随机Dirichlet级数的增长性

Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (2): 475-485.

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The Growth of Dirichlet Series and Random Dirichlet Series of Infinite Order in the Half Plane

(1. $College of Mathematics and Informatics, Shaoguan University, Guangdong Shaoguan 512005; 2. School of Mathematics, South China Normal University, Guangzhou 510631)

Received:2007-11-28 Revised:2008-10-16 Online:2009-04-25 Published:2009-04-25
Supported by:
国家自然科学基金(10471048)资助

Abstract

Abstract:

In this paper, the authors study the growth of Dirichlet series and random Dirichlet series of infinite order in the half-plane. They prove several lemmas by using the Newton polygon and type-function U( r) of Hiong Kin-lai
under a much weaker coefficient condition. And the relations between its order and low order and its coefficients are obtained. For some random Dirichlet series with non-uniformly distribution random variables there are almost surely (a.s.) same relations.

Key words: Infinite order, Dirichlet series, Random series, Type function, Growth

CLC Number:

30D25

Luo Shile; Sun Daochun. The Growth of Dirichlet Series and Random Dirichlet Series of Infinite Order in the Half Plane[J].Acta mathematica scientia,Series A, 2009, 29(2): 475-485.

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The Growth of Dirichlet Series and Random Dirichlet Series of Infinite Order in the Half Plane

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