黎曼假设及其充要条件  

THE RIEMAN HYPOTHESIS AND ITS NECESSARY AND SUFFICIENT CONDITIONS

作　　者：王可成[1] 

机构地区：[1]长沙交通学院路桥工程系

出　　处：《长沙交通学院学报》1994年第1期1-8,共8页Journal of Changsha Communications University

摘　　要：１８５９年，Ｂ．Ｒｉｅｍａｎｎ猜测Ｚｅｔａ函数ζ（ｓ）的所有非平凡零点位于临界线Ｒｅｓ＝１／２上，通常称之为黎曼假设，这是一个迄今尚未证明的著名教学问题．本文研究黎曼假设的充要条件，并指出验证该条件的困难．In 1859, Riemann Conjectured that all the nontrical zeros of the zeta - function ζ(s)should lie on the critical line Res=1/2. This hypothesis is the most celebrated open problem in mathematics. The purpose of this paper is to investigate several necessary and sufficient conditions of the Riemann hypothesis, and the difficulties have been discerned of showing whether such conditions are satisfied or not.

关 键 词：黎曼假设 充要条件 非平凡零点 临界线 

分 类 号：O156.4[理学—数学]