Acta mathematica scientia, Series B >
THE LOWER ORDER AND LINEAR ORDER OF MULTIPLE DIRICHLET SERIES
Received date: 2015-10-20
Revised date: 2016-01-28
Online published: 2017-02-25
Supported by
Research supported by the National Natural Science Foundation of China (11501127), Natural Science Foundation of Guangdong Province (2016A030313686), the Training Program for Outstanding Young Teachers in University of Guangdong Province (312XCQ14564) and Foundation for Distinguished Young Talents in Higher Education of Guangdong Province (2013LYM0027, 2014KQNCX068).
The article investigates the growth of multiple Dirichlet series. The lower order and the linear order of n-tuple Dirichlet series in Cn are defined and some relations between them and the coefficients and exponents of n-tuple Dirichlet series are obtained.
Key words： multiple Dirichlet series; lower order; linear order
Meili LIANG , Yingying HUO . THE LOWER ORDER AND LINEAR ORDER OF MULTIPLE DIRICHLET SERIES[J]. Acta mathematica scientia, Series B, 2017 , 37(1) : 131 -138 . DOI: 10.1016/S0252-9602(16)30121-7
[1] Gao Z S. The growth of entire function defined by Dirichlet series. Acta Math Sin (Chinese Series), 1999, 42:741-748
[2] Juneja O P, Prem S. On the lower order of an entire function defined by Dirichlet series. Math Ann, 1969, 184:25-29
[3] Juneja O P, Kapoor G P. On the lower order of an entire Dirichlet series. Math Ann, 1972:128-132
[4] Liang M L, Gao Z S. Convergence and growth of multiple Dirichlet series. Acta Math Sci, 2010, 30:1640-1648
[5] Sun D C, Yu J R. Sur la distribution des valeurs de certaines séries de aléatoires de Dirichlet (II). C R Acad Sci Paris, 1989, 308:205-207
[6] Valiron G. Entire functions and Borel's directions. Proc Nat Acad Sci USA, 1934, 20:211-215
[7] Yu J R. Sur la croissance de certaines séries de Dirichlet sur des semi-droites horizontales. C R Acad Sci Paris, 1983, 296:187-190
[8] Yu J R. Julia lines of random Dirichlet series. Bull Sci Math, 2004, 128:341-353
[9] Yu J R. On the growth and the distributions of values of exponential series convergent only in the right half-plane. Chin Ann Math, 1982, 3:545-554
[10] Yu J R. The convergence of Two-tuple Dirichet Series and Two-tuple Laplace Transform. J Wuhan Univ Nat Sci, 1962, 1:1-16
[11] Yu J R. Asymptotic two-tuple Dirichlet series and its application. J Wuhan Univ Nat Sci, 1963, 2:1-16
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