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.
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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