On the zeros of the Riemann zeta function in the critical strip
Author:
Richard P. Brent
Journal:
Math. Comp. 33 (1979), 13611372
MSC:
Primary 10H05
DOI:
https://doi.org/10.1090/S00255718197905379832
MathSciNet review:
537983
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Abstract  References  Similar Articles  Additional Information
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.

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Additional Information
Keywords:
Gram blocks,
Riemann hypothesis,
Riemann zeta function,
RiemannSiegel formula,
Rosser’s rule,
Turing’s theorem,
zeta functions
Article copyright:
© Copyright 1979
American Mathematical Society