Journal of Guangdong University of Technology ›› 2019, Vol. 36 ›› Issue (04): 52-58.doi: 10.12052/gdutxb.180140

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The Generalized Order of Dirichlet Series

Chen Qing-yuan, Huo Ying-ying   

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2018-10-29 Online:2019-06-18 Published:2019-05-31

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Abstract: The generalized order of Dirichlet series on the whole plane is studied. The Knopp-Kojima method is used to obtain the results of the growth relationship between the maximum modulus and the coefficients of Dirichlet series, and the above results are transformed into the relation between the coefficients of Dirichlet series and its generalized order under weak conditions.

Key words: Dirichlet series, generalized order, slow growth

CLC Number: 

  • O174.52
[1] VALIRON G. Sur l'abscisse de convergence des series de Dirichlet[J]. Bulletin de la Société Mathématique de France, 1924, 52:86-98
[2] VALIRON G. Théorie générale des séries de Dirichlet[M]. Paris:Gauthier-Villars, 1926.
[3] GU Z D, SUN D C. The growth of Dirichlet series[J]. Czechoslovak Mathematical Journal, 2010, 62(1):29-38
[4] LIANG M L, HUO Y Y. The lower order and linear order of multiple Dirichlet series[J]. Acta Mathematica Scientia, English Series, 2017, 37(1):131-138
[5] SEREMETA M N. Connection between the growth of the maximum of the modulus of an entire function and the moduli of the coefficients of its power series expansion[J]. Izvestiya Vysshikh Uchebnykh Zavedenii.Matematika, 1967, 2:100-108
[6] KAPOOR G, NAUTIYAL A. Polynomial approximation of an entire function of slow growth[J]. Journal of Approximation Theory, 1981, 32(1):64-75
[7] KONG Y Y, GAN H L. On orders and types of Dirichlet series of slow growth[J]. Turkish Journal of Mathematics, 2010, 34(1):1-12
[8] MANDELBROJT S. Dirichlet series:principles and methods[M]. Berlin:Springer Science & Business Media, 2012.
[9] KONG Y Y. On some q-orders and q-types of Dirichlet-Hadamard product function[J]. Acta Mathematica Sinica, Chinese Series, 2009, 52(6):1165-1172
[10] JIN Q Y, SUN D C. On the distribution of random Dirichlet series in the whole plane[J]. Turkish Journal of Mathematics, 2008, 32(3):245-254
[11] SHANG L N, GAO Z S. Entire functions defined by Dirichlet series[J]. Journal of Mathematical Analysis and Applications, 2008, 339(2):853-862
[12] HUO Y Y, KONG Y Y. On the generalized order of Dirichlet series[J]. Acta Mathematica Scientia, 2015, 35(1):133-139
[13] KNOPP K. Über die Konvergenzabszisse des Laplace-Integrals[J]. Mathematische Zeitschrift, 1951, 54(3):291-296
[14] HUO Y Y, KONG Y Y. On generalized orders and generalized types of Dirichlet series in the right half-plane[J]. Acta Mathematica Scientia, 2014, 34B(1):175-182
[15] 余家荣, 丁晓庆, 田范基.Dirichlet级数与随机Dirichlet级数的值分布[M].武汉:武汉大学出版社, 2004.
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