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Mathematics of Computation

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On the zeros of the Riemann zeta function in the critical strip. II

Authors: R. P. Brent, J. van de Lune, H. J. J. te Riele and D. T. Winter
Journal: Math. Comp. 39 (1982), 681-688
MSC: Primary 10H05; Secondary 10-04, 30-04
Corrigendum: Math. Comp. 46 (1986), 771.
MathSciNet review: 669660
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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 + $ 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.

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Keywords: Gram blocks, Riemann hypothesis, Riemann zeta function, Riemann-Siegel formula, Rosser's rule
Article copyright: © Copyright 1982 American Mathematical Society