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The growth of Dirichlet series

Zhendong GuDaochun Sun — 2012

Czechoslovak Mathematical Journal

We define Knopp-Kojima maximum modulus and the Knopp-Kojima maximum term of Dirichlet series on the right half plane by the method of Knopp-Kojima, and discuss the relation between them. Then we discuss the relation between the Knopp-Kojima coefficients of Dirichlet series and its Knopp-Kojima order defined by Knopp-Kojima maximum modulus. Finally, using the above results, we obtain a relation between the coefficients of the Dirichlet series and its Ritt order. This improves one of Yu Jia-Rong's...

Julia lines of general random Dirichlet series

Qiyu JinGuantie DengDaochun Sun — 2012

Czechoslovak Mathematical Journal

In this paper, we consider a random entire function f ( s , ω ) defined by a random Dirichlet series n = 1 X n ( ω ) e - λ n s where X n are independent and complex valued variables, 0 λ n + . We prove that under natural conditions, for some random entire functions of order ( R ) zero f ( s , ω ) almost surely every horizontal line is a Julia line without an exceptional value. The result improve a theorem of J. R. Yu: Julia lines of random Dirichlet series. Bull. Sci. Math. 128 (2004), 341–353, by relaxing condition on the distribution of X n for such function...

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