## 广义狄利克雷级数的收敛性质研究+文献综述

Title    Dirichlet  Series
Abstract
The main content of this article is to introduce the convergence properties of generalized Dirichlet series. by radical discrimination law and D'Alembert discrimination attempt to determine the horizontal convergence of Dirichlet series, uniform convergence and absolute convergence abscissa abscissa. And examples of convergence abscissa describes the relationship between the three.
This paper also describes the relationship between the Riemann hypothesis Dirichlet series, reflects the studies of Dirichlet series for the importance of analytic number theory. I give a brief introduction to the study of histroy Dirichlet series, The main research direction of modern Dirichlet series method and current research achievements. Later in the article also briefly introduces the random Dirichlet series, simply giving the convergence properties of Dirichlet series in the coefficient as different random variable sequences 源￥自%六^^维*论-文+网=www.lwfree.cn
Keywords  Generalized Dirichlet Series；Convergence；Riemann Hypothesis；Random Dirichlet Series

1  绪论…1
1.1狄利克雷级数与黎曼猜想1
1.2狄利克雷级数例子…2
1.3研究狄利克雷级数的意义及研究现状…3
2狄利克雷级数的解析性质…5
2.1狄利克雷级数收敛性质的简单介绍5
2.2广义狄利克雷级数其他的一些解析性质5
3  狄利克雷级数的收敛性 …8
3.1收敛域8
3.2收敛横坐标的计算11
3.3三种收敛横坐标之间的关系及例子19
4  其他一些定理性质22
4.1随机狄利克雷级数的收敛性22
4.2拉普拉斯变换与狄利克雷级数…26

1     绪论
1.1  狄利克雷级数与黎曼猜想

1859年黎曼写了一篇题为“论小于给定数值的素数个数”的论文。这篇长度只有八页的短小论文，就是今天我们所说的黎曼猜想的“诞生地”[3]。黎曼的这篇文章的成果十分重大，但虽然如此，但由于其精短的篇幅，文字极为简练，甚至可以说简练得有些过分[3]。因为这篇论文中包括了很多“证明从略”的地方。而在这些“证明从略”的地方当中，有些甚至花费了后世数学家们几十年的努力才得以补全完善，而有些甚至直到今日仍是还没有人给出完善的证明[3]。 广义狄利克雷级数的收敛性质研究+文献综述:http://www.lwfree.cn/shuxue/20180817/21544.html
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