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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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On the zeros of the Riemann zeta function in the critical strip. II
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by R. P. Brent, J. van de Lune, H. J. J. te Riele and D. T. Winter PDF
Math. Comp. 39 (1982), 681-688 Request permission

Corrigendum: Math. Comp. 46 (1986), 771.


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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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 39 (1982), 681-688
  • MSC: Primary 10H05; Secondary 10-04, 30-04
  • DOI:
  • MathSciNet review: 669660