| Title:
|
The growth of a class of random Dirichlet series on the horizontal zone (English) |
| Author:
|
Gu, Zhendong |
| Author:
|
Sun, Daochun |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
137 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
65-77 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper we obtain that, under some condition, the Rademacher-Dirichlet series or the Steinhaus-Dirichlet series on the whole plane and on the horizontal zone almost surely have the same growth. (English) |
| Keyword:
|
random Dirichlet series |
| Keyword:
|
Rademacher-Dirichlet series |
| Keyword:
|
Steinhaus-Dirichlet series |
| Keyword:
|
growth |
| MSC:
|
30B20 |
| MSC:
|
30B50 |
| idZBL:
|
Zbl 1249.30002 |
| idMR:
|
MR2978446 |
| DOI:
|
10.21136/MB.2012.142788 |
| . |
| Date available:
|
2012-04-19T00:02:12Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142788 |
| . |
| Reference:
|
[1] Kawata, T.: Fourier Analysis in Probability Theory.New York, Acad. Press (1972). Zbl 0271.60022, MR 0464353 |
| Reference:
|
[2] Reac, Paley, Zygmund, A.: On some series of functions (1), (2), (3).Proc. Camb. Phil. Soc. 26 (1930) 337-357, 458-474; 28 (1932), 190-205. 10.1017/S0305004100016078 |
| Reference:
|
[3] Bohr, H.: Collected Mathematical Works.Dansk Matematisk Forening Copenhagen (1952). Zbl 0049.00105, MR 0057790 |
| Reference:
|
[4] Jiarong, Yu: Some properties of random Dirichlet series.Acta Math. Sin. 21 (1978), 97-118 Chinese. MR 0507192 |
| Reference:
|
[5] Knopp, K.: Über de Konvergenzabscisse des Laplace-Integrals.Math. Z. (1951), 54 291-296 German. MR 0042539 |
| Reference:
|
[6] Valiron, G.: Sur l'abscisse de convergence des séries de Dirichlet.Bulletin de la Société Mathématique de France 52 (1924), 166-174 French. MR 1504844, 10.24033/bsmf.1051 |
| Reference:
|
[7] Tanaka, C.: Note on Dirichlet series (V), On the integral functions defined by Dirichlet series (I).Tôhoku Math. J., II. Ser. (1953), 5 67-78. Zbl 0053.37502, MR 0057320 |
| Reference:
|
[8] Valiron, G.: Théorie genérale des séries de Dirichlet.Mémorial des sciences mathématiques, Fasc. 17 (1926), French. |
| Reference:
|
[9] Valiron, G.: Entire functions and Borel's directions.Proc. Nat. Acad. Sci. USA (1934), 20 211-215. Zbl 0009.02503 |
| . |
