On the zeros of the Riemann zeta function in the critical strip
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- by Richard P. Brent PDF
- Math. Comp. 33 (1979), 1361-1372 Request permission
Abstract:
We describe a computation which shows that the Riemann zeta function $\zeta (s)$ has exactly 75,000,000 zeros of the form $\sigma + it$ it in the region $0 < t < 32,585,736.4$; all these zeros are simple and lie on the line $\sigma = 1/2$. (A similar result for the first 3,500,000 zeros was established by Rosser, Yohe and Schoenfeld.) Counts of the number of Gram blocks of various types and the number of failures of "Rosser’s rule" are given.References
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Math. Comp. 33 (1979), 1361-1372
- MSC: Primary 10H05
- DOI: https://doi.org/10.1090/S0025-5718-1979-0537983-2
- MathSciNet review: 537983