On the zeros of the Riemann zeta function in the critical strip
On the zeros of the Riemann zeta function in the critical strip
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关于临界带中黎曼 zeta 函数的零点
DOI：
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发表时间：
1979
期刊：
影响因子：
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通讯作者：
R. Brent
中科院分区：
文献类型：
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作者：
R. Brent
我们描述了一个计算，它表明黎曼zeta函数在0 < t <32，585，736.4的范围内，恰好有75，000，000个形式为σ+ it的零点;所有这些零点都是单零点，位于直线σ = 1/2上。（Rosser、Yohe和Schoenfeld对前3，500，000个零也得出了类似的结果。给出了各种类型的格兰姆块数和“Rosser规则”失效的次数。评论这里只给出摘要。全文如[1]所示。进一步的工作，见[2，3]。
We describe a computation which shows that the Riemann zeta function ζ(s) has exactly 75,000,000 zeros of the form σ+ it in the region 0 < t < 32,585,736.4; all these zeros are simple and lie on the line σ = 1/2. (A similar result for the first 3,500,000 zeros was established by Rosser, Yohe and Schoenfeld.) Counts of the number of Gram blocks of various types and the number of failures of “Rosser’s rule” are given. Comments Only the Abstract is given here. The full paper appeared as [1]. For further work, see [2, 3].