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), 681688
MSC:
Primary 10H05; Secondary 1004, 3004
DOI:
https://doi.org/10.1090/S00255718198206696601
Corrigendum:
Math. Comp. 46 (1986), 771.
MathSciNet review:
669660
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Abstract  References  Similar Articles  Additional Information
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. 13611372.) Counts of the numbers of Gram blocks of various types and the failures of "Rosser’s rule" are given.

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Additional Information
Keywords:
Gram blocks,
Riemann hypothesis,
Riemann zeta function,
RiemannSiegel formula,
Rosser’s rule
Article copyright:
© Copyright 1982
American Mathematical Society