| Title:
|
Julia lines of general random Dirichlet series (English) |
| Author:
|
Jin, Qiyu |
| Author:
|
Deng, Guantie |
| Author:
|
Sun, Daochun |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
4 |
| Year:
|
2012 |
| Pages:
|
919-936 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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\leq \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. (English) |
| Keyword:
|
random Dirichlet series |
| Keyword:
|
order $(R)$ |
| Keyword:
|
Julia lines |
| Keyword:
|
entire function |
| MSC:
|
30B20 |
| MSC:
|
30B50 |
| MSC:
|
30D05 |
| MSC:
|
30D20 |
| MSC:
|
30D35 |
| MSC:
|
60G99 |
| idZBL:
|
Zbl 1274.30106 |
| idMR:
|
MR3010248 |
| DOI:
|
10.1007/s10587-012-0074-x |
| . |
| Date available:
|
2012-11-10T21:31:07Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143036 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
|
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