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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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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

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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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 39 (1982), 681-688
  • MSC: Primary 10H05; Secondary 10-04, 30-04
  • DOI: https://doi.org/10.1090/S0025-5718-1982-0669660-1
  • MathSciNet review: 669660