零级Dirichet级数的增长性及其Dirichlet-Hadamard乘积
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摘要
本文研究了全平面上零级Dirichlet级数的增长性的问题.利用复级数理论,进一步讨论了在两种条件下Dirichlet级数的Dirichlet-Hadamard乘积的增长性,获得了零级Dirichlet级数及其Dirichlet-Hadamard乘积涉及对数级与对数型的几个关系定理,推广了孔荫莹等人的结果.
The main purpose of this paper is to investigate the growth of Dirichlet series with zero order which converges in the whole complex plane. By using the theory of complex series, we further study the growth of Dirichlet-Hadamard product of Dirichlet series with zero order under two different conditions. Some relationship theorems concerning logarithmic order and logarithmic type between Dirichlet series and its Dirichlet-Hadamard product are obtained,which are improvement and extension of previous results given by Kong.
The main purpose of this paper is to investigate the growth of Dirichlet series with zero order which converges in the whole complex plane. By using the theory of complex series, we further study the growth of Dirichlet-Hadamard product of Dirichlet series with zero order under two different conditions. Some relationship theorems concerning logarithmic order and logarithmic type between Dirichlet series and its Dirichlet-Hadamard product are obtained,which are improvement and extension of previous results given by Kong.
引文
[1]Hardy G H,Riesz M.The general theory of Dirichlet series[M].New York:Stechert-Hafner,Inc,1964.
[2]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.
[3]田宏根,孙道椿,郑承民.平面上的零级Dirichlet级数[J].系统科学与数学,2006,26(3):270-276.
[4]高宗升.Dirichlet级数表示的整函数的增长性[J].数学学报,1999,42(4):741-748.
[5]高宗升,孙道椿.无限级随机Dirichlet级数的值分布[J].数学年刊,1993,14(6):677-685.
[6]贺隆贞.关于狄里克莱级数确定的整函数的(p,q)(R)型和下(p,q))(R)型[J].武汉大学学报(自然科学版),1985,4:17-26.
[7]贺隆贞.关于狄里克莱级数确定的整函数的(p,q)(R)级和下(p,q)(R)型[J].武汉大学学报(自然科学版),1983,3:73-89.
[8]Sayyed K A M,Metwally M S.Logarithmic order and logarithmic type of functions and sets of polynomials of two complex variables[J].Bull.Fac.Fac.Sci.Qena(Egypt),1994,2(2):127-140.
[9]孔荫莹.Dirichlet-Hadamard乘积的q-级与q-型[J].数学学报,2009,52(6):1165-1172.
[10]孔荫莹,邓冠铁.Dirichlet级数的Dirichlet-Hadamard乘积[J].数学年刊,2014,35(2):145-152.
[11]崔永琴,汤文菊,徐洪焱.Dirichlet级数及其新型Dirichlet-Hadamard乘积的增长性[J].数学的实践与认识,2015,45(22):267-273.
[2]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.
[3]田宏根,孙道椿,郑承民.平面上的零级Dirichlet级数[J].系统科学与数学,2006,26(3):270-276.
[4]高宗升.Dirichlet级数表示的整函数的增长性[J].数学学报,1999,42(4):741-748.
[5]高宗升,孙道椿.无限级随机Dirichlet级数的值分布[J].数学年刊,1993,14(6):677-685.
[6]贺隆贞.关于狄里克莱级数确定的整函数的(p,q)(R)型和下(p,q))(R)型[J].武汉大学学报(自然科学版),1985,4:17-26.
[7]贺隆贞.关于狄里克莱级数确定的整函数的(p,q)(R)级和下(p,q)(R)型[J].武汉大学学报(自然科学版),1983,3:73-89.
[8]Sayyed K A M,Metwally M S.Logarithmic order and logarithmic type of functions and sets of polynomials of two complex variables[J].Bull.Fac.Fac.Sci.Qena(Egypt),1994,2(2):127-140.
[9]孔荫莹.Dirichlet-Hadamard乘积的q-级与q-型[J].数学学报,2009,52(6):1165-1172.
[10]孔荫莹,邓冠铁.Dirichlet级数的Dirichlet-Hadamard乘积[J].数学年刊,2014,35(2):145-152.
[11]崔永琴,汤文菊,徐洪焱.Dirichlet级数及其新型Dirichlet-Hadamard乘积的增长性[J].数学的实践与认识,2015,45(22):267-273.