Geodesic
The growth of Dirichlet series
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 1, pp. 29-38
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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.
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.
DOI : 10.1007/s10587-012-0014-9
Classification : 30B50
Keywords: Dirichlet series; order; abscissa of convergence 
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Gu, Zhendong; Sun, Daochun. The growth of Dirichlet series. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 1, pp. 29-38. doi: 10.1007/s10587-012-0014-9

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