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

Brent, R. P.; van de Lune, J.; te Riele, H. J. J.; Winter, D. T.

doi:10.1090/S0025-5718-1982-0669660-1

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.

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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