【作者】 晁志英；

【导师】 田宏根；

【作者基本信息】 新疆师范大学 ， 基础数学， 2007， 硕士

【摘要】 本文研究了平面上狄里克莱级数和随机狄里克莱级数的增长性。全文共分两个部分:1.全平面上的零级狄里克莱级数2.半平面上的狄里克莱级数和随机狄里克莱级数文章第一部分参考熊庆来的型函数引入函数U( x ) ( x = e~σ),并给出了狄里克莱级数正规增长的定义,研究了全平面上零级狄里克莱级数的增长性并得到了全平面上零级狄里克莱级数正规增长的充要条件,即文中定理1.1和定理1.2;在文章第二部分,对右半平面上的狄里克莱级数和随机狄里克莱级数增长性进行研究,引入指标,得到了零级狄里克莱级数增长性的一个充要条件,并研究了有限级和无穷级狄里克莱级数和随机狄里克莱级数在条件减弱后,即在条件下的增长性,即文中定理2.3,定理2.4和定理2.5。更多还原

【Abstract】 This paper studies the growth of Dirichlet series and random Dirichlet series in the plane. The full text is divided into two parts :1. Zero order Dirichlet series in the whole plane.2. Dirichlet series and random Dirichlet series in the half PlaneThe first part of this article introduce the function U( x ) (x = e~σ) followed type function obtained by Qinglai xiong, and gives the Dirichlet series the informal definition of normal growth, Study the growth of zero-order Dirichlet series in the the whole plane and obtain a necessary and sufficient condition on the zero- order Dirichlet series ,that is Theorem 1.1 and theorem 1.2 in the text; In addition, The paper study the growth of of the Dirichlet series and random Dirichlet series on the right half-plane in the second part of this article , and obtain a necessary and sufficient conditions on the growth of zero-order Dirichlet series by introducing the Indicator ; we also study the growth of the finite-and infinite - Dirichlet series and random Dirichlet series in the weakened conditions, that is (0 <ρ<+∞)we obtain the Theorem 2.3, theorem 2.4 and theorem 2.5 in the text under this condition.更多还原