Julia lines of general random Dirichlet series

Qiyu Jin; Guantie Deng; Daochun Sun

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 4, page 919-936
  • ISSN: 0011-4642

Abstract

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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 f ( s , ω ) of order ( R ) zero, almost surely.

How to cite

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Jin, Qiyu, Deng, Guantie, and Sun, Daochun. "Julia lines of general random Dirichlet series." Czechoslovak Mathematical Journal 62.4 (2012): 919-936. <http://eudml.org/doc/246481>.

@article{Jin2012,
abstract = {In this paper, we consider a random entire function $f(s,\omega )$ defined by a random Dirichlet series $\sum \nolimits _\{n=1\}^\{\infty \}X_n(\omega ) \{\rm e\} ^\{-\lambda _n s\}$ where $X_n$ are independent and complex valued variables, $0\le \lambda _n \nearrow +\infty $. We prove that under natural conditions, for some random entire functions of order $(R)$ zero $f(s,\omega )$ 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 $f(s,\omega )$ of order $(R)$ zero, almost surely.},
author = {Jin, Qiyu, Deng, Guantie, Sun, Daochun},
journal = {Czechoslovak Mathematical Journal},
keywords = {random Dirichlet series; order $(R)$; Julia lines; entire function; random Dirichlet series; Julia lines; entire function},
language = {eng},
number = {4},
pages = {919-936},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Julia lines of general random Dirichlet series},
url = {http://eudml.org/doc/246481},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Jin, Qiyu
AU - Deng, Guantie
AU - Sun, Daochun
TI - Julia lines of general random Dirichlet series
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 4
SP - 919
EP - 936
AB - In this paper, we consider a random entire function $f(s,\omega )$ defined by a random Dirichlet series $\sum \nolimits _{n=1}^{\infty }X_n(\omega ) {\rm e} ^{-\lambda _n s}$ where $X_n$ are independent and complex valued variables, $0\le \lambda _n \nearrow +\infty $. We prove that under natural conditions, for some random entire functions of order $(R)$ zero $f(s,\omega )$ 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 $f(s,\omega )$ of order $(R)$ zero, almost surely.
LA - eng
KW - random Dirichlet series; order $(R)$; Julia lines; entire function; random Dirichlet series; Julia lines; entire function
UR - http://eudml.org/doc/246481
ER -

References

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