复指数Dirichlet 级数表示的整函数

该文对一个由复指数Dirichlet 级数表示的，其系数满足一给定增长条件且在一固定水平带形有界不恒为零的整函数的存在性， 给出了充分必要条件。     

Estimation over Curves of the Functions Given by Dirichlet Series on a Half-Plane

We study the maximal term of the Hadamard composition of Dirichlet series with real exponents. We obtain a lower estimate for the sum of a Dirichlet series over a curve arbitrarily approaching the convergence line.     

Asymptotic Behavior of the Sum of the Dirichlet Series of Prescribed Growth on Curves

We study the relationship between the growth and decrease of the sum of the entire Dirichlet series of finite order (in the sense of Ritt) on arbitrary curves going to infinity. For a class of exponents having a regular distribution (in a certain sense), we obtain a test for the logarithm of the maximal term to be equivalent to the logarithm of the absolute value of the sum of the Dirichlet series on at least one unbounded sequence of points of the curve.__________Translated from Matematicheskie Zametki, vol. 78, no. 1, 2005, pp. 37–51.Original Russian Text Copyright © 2005 by A. M. Gaisin, I. D. Latypov.     

On the Young Conjugate Functions and the Behavior of the Maximal Terms of the Derivatives of Dirichlet Series

We obtain a criterion for the growth of the maximal term of the Dirichlet series with positive exponents in terms of the behavior of the maximal terms of the successive derivatives of this series. This criterion is obtained from a more general result concerning Young conjugate functions proved in this paper.     

Global analyticity of solutions of nonlinear functional differential equations representable by Dirichlet series

We show that, under certain additional assumptions, analytic solutions of sufficiently general nonlinear functional differential equations are representable by Dirichlet series of unique structure on the entire real axis ℝ and, in some cases, on the entire complex plane ℂ. We investigate the dependence of these solutions on the coefficients of the basic exponents of the expansion into a Dirichlet series. We obtain sufficient conditions for the representability of solutions of the main initial-value problem by series of exponents. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 9, pp. 1276–1284, September, 2006.     

關於廣義狄黎希萊級數的若干問題

<正> 導言 在本文中所謂廣義狄黎希萊級數就是指具有複指數的狄黎希萊級數.黎提在研究常係數無限級線性齊次方程時討論到有間隙的這種級數。希爾與隆茨分別獨立地研究過它的收斂區域,並且獲得了若干共同的結果.范禮隆將黎提與希爾的結果加以推廣,並且研究由這種級數所定義的整函數,特     

CONVERGENCE AND GROWTH OF MULTIPLE DIRICHLET SERIES

This article investigates the convergence and growth of multiple Dirichlet series. The Valiron formula of Dirichlet series is extended to n-tuple Dirichlet series and an equivalence relation between the order of n-tuple Dirichlet series and its coefficients and exponents is obtained.     

Convergence and growth of multiple Dirichlet series

This article investigates the convergence and growth of multiple Dirichlet series. The Valiron formula of Dirichlet series is extended to n-tuple Dirichlet series and an equivalence relation between the order of n-tuple Dirichlet series and its coefficients and exponents is obtained.     

The lower order and linear order of multiple dirichlet series

The article investigates the growth of multiple Dirichlet series.The lower order and the linear order of n-tuple Dirichlet series in C~n are defined and some relations between them and the coefficients and exponents of n-tuple Dirichlet series are obtained.     

The representation of regular functions by Dirichlet series

It is proved that if a system of exponents has the property that any function regular in a closed convex domain ¯G can be represented in an open domain G by a Dirichlet series, then any function regular only in G can be represented in G by a Dirichlet series with the same system of exponents. A study is made of the representation of functions regular in ¯G by Dirichlet series that converge in ¯G.Translated from Matematicheskie Zametki, Vol. 21, No. 5, pp. 641–651, May, 1977.     

ON ORDER AND TYPE OF MULTIPLE DIRICHLET SERIES

This article investigates the growth of multiple Dirichlet series.The order and the type of n-tuple Dirichlet series in C~n are defined and some relations between them and the coefficients and exponents of n-tuple Dirichlet series are obtained,which generalize some results about simple Dirichlet series of Lindelof and Pringsheim.     

On convergence and growth of multiple dirichlet series

In the present paper, the Valiron formula of simple Dirichlet series is extended to n-tuple Dirichlet series. And an equivalence relation between the order of n-tuple Dirichlet series and its coefficients and exponents is obtained.     

Divergence of the Fourier series by generalized Haar systems at points of continuity of a function

We obtain a connection between the Dirichlet kernels and partial Fourier sums by generalized Haar and Walsh (Price) systems. Based on this, we establish an interrelation between convergence of the Fourier series by generalized Haar and Walsh (Price) systems. For any unbounded sequence we construct a model of continuous function on a group (and even on a segment [0, 1]), whose Fourier series by generalized Haar system generated by this sequence, diverges at some point.     

On the representation of functions by Dirichlet double series

We consider the problem of representing regular functions of two complex variables by Dirichlet double series with complex exponents.Translated from Matematicheski Zametki, Vol. 7, No. 1, pp. 53–61, January, 1970.     

B-Stability of the Maximal Term of the Hadamard Composition of Two Dirichlet Series

We establish a criterion for the logarithm of the maximal term of a Dirichlet series whose absolute convergence domain is a half-plane to be equivalent to the logarithm of the maximal term of its Hadamard composition with another Dirichlet series of some class on the asymptotic set.     

On the Maximum of the Modulus and the Maximal Term of Dirichlet Series

For the Dirichlet series, we obtain a condition on the exponents for which the logarithms of the maximum of the modulus of its sum and of the maximal term are equivalent to the same convex function.     

随机Dirichlet级数的奇异点和Picard点

本文研究系数为鞅差序列的随机Ｄｉｒｉｃｈｌｅｔ级数的奇异点和Ｐｉｃａｒｄ点。     

二重 Dirichlet级数的增长性

首先研究了双平面上二重Dirichlet级数的系数和指数与增长性之间的关系, 得到了θ 线性下级的一个充要条件, 然后在适当的条件下, 对二重Dirichlet级数所确定的整函数在双水平直线上的θ 线性级进行了估计.     

零级缺项广义Dirichlet级数的增长性

在一定的指数条件下,研究了全平面上零级广义Dirichlet级数的增长性,得到了关于它的系数和指数与增长级之间关系的结论.     

THE VALUE DISTRIBUTION OF RANDOM ANALYTIC DIRICHLET SERIES OF NEUTRAL GROWTH(I)

1IntroductionandtheMainResultTheBorelpointsofrandomanajyticDirichletserieshavebeenstudied[1'2]oilthecon(litiollthatthecoefficientsoftherandomDirichletseriesareindependentrandomvariables,sucfl;lstheRademacliersequencettheSteinhausesequence!andtheN-sequence.[1]Thepresentpaperdealswiththesimilarproblem,andintendstoobtainmoreaccurate(inasence)resultthan[2,Theorem4]evenifthecoefficientsofrandomDirichletseriesareassumedtobeamartingaledifferencesequence.ConsidertherandomDirichletseriesfi(s)=Zn=I…