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Journal Article
On the Zeros of the Riemann Zeta Function in the Critical Strip. II
R. P. Brent, J. van de Lune, H. J. J. te Riele and D. T. Winter
Mathematics of Computation
Vol. 39, No. 160 (Oct., 1982), pp. 681-688
Published
by: American Mathematical Society
DOI: 10.2307/2007345
https://www.jstor.org/stable/2007345
Page Count: 8
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Abstract
We describe extensive computations which show that Riemann's zeta function $\zeta(s)$ has exactly 200,000,001 zeros of the form $\sigma + it$ in the region $0 < t < 81,702,130.19$; all these zeros are simple and lie on the line $\sigma = \frac{1}{2}$. (This extends a similar result for the first 81,000,001 zeros, established by Brent in Math. Comp., v. 33, 1979, pp. 1361-1372.) Counts of the numbers of Gram blocks of various types and the failures of "Rosser's rule" are given.
Mathematics of Computation
© 1982 American Mathematical Society