A Joint Limit Theorem for General Dirichlet Series

In this paper, a joint limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for general Dirichlet series is proved. The explicit form of the limit measure is given.     

A Joint Limit Theorem for General Dirichlet Series

We obtain a joint limit theorem in the sense of weak convergence of probability measures for general Dirichlet series in the space of meromorphic functions.     

Mixed Siegel Modular Forms and Special Valuesof Certain Dirichlet Series

 Let be a Siegel modular form of weight ?, and let be an Eichler embedding, where denotes the Siegel upper half space of degree n. We use the notion of mixed Siegel modular forms to construct the linear map of the spaces of Siegel cusp forms for the congruence subgroup and express the Fourier coefficients of the image of an element under in terms of special values of a certain Dirichlet series. We also discuss connections between mixed Siegel cusp forms and holomorphic forms on a family of abelian varieties. (Received 28 February 2000; in revised form 11 July 2000)     

Mixed Siegel Modular Forms and Special Valuesof Certain Dirichlet Series

 Let be a Siegel modular form of weight ?, and let be an Eichler embedding, where denotes the Siegel upper half space of degree n. We use the notion of mixed Siegel modular forms to construct the linear map of the spaces of Siegel cusp forms for the congruence subgroup and express the Fourier coefficients of the image of an element under in terms of special values of a certain Dirichlet series. We also discuss connections between mixed Siegel cusp forms and holomorphic forms on a family of abelian varieties.     

有限级Dirchlet级数及随机Dirchlet级数

本文研究了全平面上有限级Dirichlet级数的增长性和正规增长性,得到了两个充要条 件;证明了有限级随机Dirichlet级数的增长性几乎必然与其在每条水平直线上的增长性相同．     

有限级Dirichlet级数及随机Dirichlet级数

本文研究了全平面上有限级Dirichlet级数的增长性和正规增长性,得到了两个充要条件;证明了有限级随机Dirichlet级数的增长性几乎必然与其在每条水平直线上的增长性相同.     

Restricted Universality of Power Series

We prove the existence of a power series having radius of convergence0, whose partial sums have universal approximation propertieson any compact set with connected complement that is containedin a finite union of circles centred at 0 and having rationalradii, but do not have such properties on any compact set withnonempty interior. This relates to a theorem of A. I. Seleznev.2000 Mathematics Subject Classification 30B30 (primary), 30B10,30E60 (secondary).     

A Joint Limit Theorem on the Complex Plane for General Dirichlet Series

We prove a joint two-dimensional limit theorem in the sense of weak convergence of probability measures on the complex plane for general Dirichlet series.     

随机狄里克莱级数

该文研究了系数为ψ-混合序列随机Dirichlet级数在半平面上的收敛性和增长性,得到了比较好的结果．     

Joint Discrete Limit Theorems on the Complex Plane for General Dirichlet Series

We prove a joint discrete limit theorem in the sense of weak convergence on the complex plane for general Dirichlet series.     

Overconvergence Properties of Dirichlet Series

Potential Analysis - In this paper we use potential theoretic arguments to establish new results concerning the overconvergence of Dirichlet series. Let ${\sum }_{j=0}^{\infty } a_{j}e^{-\lambda...     

A Joint Discrete Limit Theorem in the Space of Meromorphic Functions for General Dirichlet Series

A joint discrete limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for general Dirichlet series is proved.     

On Joint Universality of the Riemann Zeta-Function

Mathematical Notes - A theorem is obtained on the approximation of a collection of analytic functions in short intervals by a collection of shifts of the Riemann zeta-function...     

Regularly Increasing Entire Dirichlet Series

For entire Dirichlet series, we establish conditions on its coefficients and exponents under which the logarithms of the maximal term and of the maximum of the modulus are regularly varying functions of order [1, + ) and the central exponent is a regularly varying function of order – 1.     

B-值双随机Dirchlet级数的收敛性

主要研究了B-值双随机Dirichlet级数在不同条件(i){Xn}服从强大数定律,且 (ii){Xn}独立不同分布,且 等条件下的收敛性,得出了收敛横坐标的简洁公式．     

Dirichlet级数的下级

采用Knopp-Kojima的方法,去掉-lim n→∞ lnn/λn=E＜+∞等条件,研究了一般的Dirichlet级数在全平面内与右半平面内的下级,给出了下级由系数表示的充要条件.     

Series Acceleration Formulas for Dirichlet Series with Periodic Coefficients

Series acceleration formulas are obtained for Dirichlet series with periodic coefficients. Special cases include Ramanujan's formula for the values of the Riemann zeta function at the odd positive integers exceeding two, and related formulas for values of Dirichlet L-series and the Lerch zeta function.     

Dirichlet Series and Curious infinite Products

By number-theoretical methods we give a result generalizingthose of J. O. Shallit, one particular case of which reads asfollows: ...=2^–;, where a(n) is equal to 1 if the sum of the digits of n in basetwo is even, and – 1 if this sum is odd. Moreover we provea conjecture of Shallit concerning a way of approximating 2^–