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arXiv 0705.45932007-05math.GM

关于黎曼ζ函数（IV）-- V

On the Riemann zeta-function, Parts IV-V

Anthony Csizmazia

备注：: 12 pages Added Part V to a contracted version of Part IV

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摘要：

在第一部分中，我们从取值于半加s的黎曼ζ函数构造了一个奇亚纯函数f（s）。假设黎曼假设与作者在第一部分提出的假设是一致的。在第四部分中，我们导出f（s）在所有s的开垂直带V上的双边拉普拉斯变换表示，其中s的实部在0和4之间。一个附加的假设被用来证明f（s）在带V上的拉普拉斯密度是正的。设z（n）是正虚部黎曼ζ函数的第n个临界零点，其值为正虚部函数的数量级。在第五部分中，导出了z（1）的表达式。一个关系得到的对z（n）和一阶导数的zeta函数到前面这样的对。

英文摘要：

In Part I an odd meromorphic function f(s) has been constructed from the Riemann zeta-function evaluated at one-half plus s. The conjunction of the Riemann hypothesis and hypotheses advanced by the author in Part I is assumed. In Part IV we derive the two-sided Laplace transform representation of f(s) on the open vertical strip V of all s with real part between zero and four. An additional hypothesis is used to prove that the Laplace density of f(s) on the strip V is positive. Let z(n) be the nth critical zero of the Riemann zeta-function of positive imaginary part in order of magnitude thereof. In Part V an expression is derived for z(1). A relation is obtained of the pair z(n) and the first derivative thereat of the zeta-function to the preceding such pairs.

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