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The growth of Dirichlet series

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, People’s Republic of China, Postal Code 510631

    Zhendong Gu & Daochun Sun

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  1. Zhendong Gu
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  2. Daochun Sun
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Correspondence to Zhendong Gu.

Additional information

Research was supported by the National Natural Science Foundation of China No. 11101096.

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Gu, Z., Sun, D. The growth of Dirichlet series. Czech Math J 62, 29–38 (2012). https://doi.org/10.1007/s10587-012-0014-9

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