| Title:
|
The growth of Dirichlet series (English) |
| Author:
|
Gu, Zhendong |
| Author:
|
Sun, Daochun |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
29-38 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 results, published in Acta Mathematica Sinica 21 (1978), 97–118. We also give two examples to show that the condition under which the main result holds can not be weakened. (English) |
| Keyword:
|
Dirichlet series |
| Keyword:
|
order |
| Keyword:
|
abscissa of convergence |
| MSC:
|
30B50 |
| idZBL:
|
Zbl 1249.30004 |
| idMR:
|
MR2899732 |
| DOI:
|
10.1007/s10587-012-0014-9 |
| . |
| Date available:
|
2012-03-05T07:08:36Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142038 |
| . |
| 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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[12] Valiron, G.: Théorie Générale des Séries de Dirichlet.Paris, Gauthier-Villars (Mémorial des sciences mathématiques, fasc. 17) (1926), French pp. 56. |
| Reference:
|
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| Reference:
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| Reference:
|
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| . |
