This note deals with the growth of entire Dirichlet series of order zero and the coefficient characteristic of the type under a kind of weaker exponent condition, and improves some known results. Moreover, the regular...This note deals with the growth of entire Dirichlet series of order zero and the coefficient characteristic of the type under a kind of weaker exponent condition, and improves some known results. Moreover, the regular growth of the series is considered under the same exponent condition, and a sufficient condition of the regular growth is given.展开更多
Under the conditions(without independence): (i) There Exists alpha > 0, such that sup E\Z(n)\(alpha) < +infinity, (ii) There Exists beta > 0, such that sup E\Z(n)\(-beta) < +infinity, the random series Sig...Under the conditions(without independence): (i) There Exists alpha > 0, such that sup E\Z(n)\(alpha) < +infinity, (ii) There Exists beta > 0, such that sup E\Z(n)\(-beta) < +infinity, the random series Sigma a(n) Z(n)e(-lambda n) and series' Sigma a(n)e(-lambda ns) a.s. have the same abscissa of convergence, the (R) order, lower order and type.展开更多
In this paper, the property of infinite order Dirichlet series in the half-plane are investigated. The more exact growth of infinite order Dirichlet series is obtained without using logarithm argument to the type-func...In this paper, the property of infinite order Dirichlet series in the half-plane are investigated. The more exact growth of infinite order Dirichlet series is obtained without using logarithm argument to the type-function for the first time.展开更多
This note implies only a moment condition upon the coefficients of random Dirichlet series to study the convergence and growth of the series. The condition needs the coefficients to satisfy the so-called inverse H?lde...This note implies only a moment condition upon the coefficients of random Dirichlet series to study the convergence and growth of the series. The condition needs the coefficients to satisfy the so-called inverse H?lder inequality, which need not be independent. The note uses a method whose feature is to compare the convergence of two series, and obtains two theorems, one dealing with the convergence of the random Dirichlet series, another the growth of the random analytic function represented by the series. These results can be used to improve essentially some known conclusions.展开更多
This paper first studies the relations between the growth and the coefficients of Dirichlet series of zero order in the whole plane,and further proves that the growth of random entire functions defined by random Diri...This paper first studies the relations between the growth and the coefficients of Dirichlet series of zero order in the whole plane,and further proves that the growth of random entire functions defined by random Dirichlet series of zero order in every horizotal straight lines is almost surely equal to the growth of entire functions defined by their corresponding Dirichlet series.展开更多
In the paper, generalized orders and generalized types of Dirichlet series in the right half-plane are given. Some interesting relationships on maximum modulus, the maximum term and the coefficients of entire function...In the paper, generalized orders and generalized types of Dirichlet series in the right half-plane are given. Some interesting relationships on maximum modulus, the maximum term and the coefficients of entire function defined by Dirichlet series of in the right half-plane are obtained.展开更多
For a given Dirichlet series absolutely convergent and of order (R)p∈(o, +) in the right-halfplan, its terms can be multiplied respectively by the members of a suitable sequence defined ina probability or topological...For a given Dirichlet series absolutely convergent and of order (R)p∈(o, +) in the right-halfplan, its terms can be multiplied respectively by the members of a suitable sequence defined ina probability or topological space such that the series obtained is of order (R)ρ on any one ofcountably infinite horizontal haif lines almost or quasi surely.展开更多
文摘This note deals with the growth of entire Dirichlet series of order zero and the coefficient characteristic of the type under a kind of weaker exponent condition, and improves some known results. Moreover, the regular growth of the series is considered under the same exponent condition, and a sufficient condition of the regular growth is given.
文摘Under the conditions(without independence): (i) There Exists alpha > 0, such that sup E\Z(n)\(alpha) < +infinity, (ii) There Exists beta > 0, such that sup E\Z(n)\(-beta) < +infinity, the random series Sigma a(n) Z(n)e(-lambda n) and series' Sigma a(n)e(-lambda ns) a.s. have the same abscissa of convergence, the (R) order, lower order and type.
基金Research supported by the national natural Science foundation ofChina(19971029)guangdong provincial natural science foundation(990444)
文摘In this paper, the property of infinite order Dirichlet series in the half-plane are investigated. The more exact growth of infinite order Dirichlet series is obtained without using logarithm argument to the type-function for the first time.
文摘This note implies only a moment condition upon the coefficients of random Dirichlet series to study the convergence and growth of the series. The condition needs the coefficients to satisfy the so-called inverse H?lder inequality, which need not be independent. The note uses a method whose feature is to compare the convergence of two series, and obtains two theorems, one dealing with the convergence of the random Dirichlet series, another the growth of the random analytic function represented by the series. These results can be used to improve essentially some known conclusions.
文摘This paper first studies the relations between the growth and the coefficients of Dirichlet series of zero order in the whole plane,and further proves that the growth of random entire functions defined by random Dirichlet series of zero order in every horizotal straight lines is almost surely equal to the growth of entire functions defined by their corresponding Dirichlet series.
基金supported by the National Natural Science Foundation of China(1110109611201083)+1 种基金Guangdong Natural Science Foundation(S2012010010376)the Startup Foundation for Doctors of Guangdong University of Technology(083063)
文摘In the paper, generalized orders and generalized types of Dirichlet series in the right half-plane are given. Some interesting relationships on maximum modulus, the maximum term and the coefficients of entire function defined by Dirichlet series of in the right half-plane are obtained.
文摘For a given Dirichlet series absolutely convergent and of order (R)p∈(o, +) in the right-halfplan, its terms can be multiplied respectively by the members of a suitable sequence defined ina probability or topological space such that the series obtained is of order (R)ρ on any one ofcountably infinite horizontal haif lines almost or quasi surely.
