On the zeros of the Riemann zeta function in the critical strip
Author:
Richard P. Brent
Journal:
Math. Comp. 33 (1979), 1361-1372
MSC:
Primary 10H05
DOI:
https://doi.org/10.1090/S0025-5718-1979-0537983-2
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 has exactly 75,000,000 zeros of the form
it in the region
; all these zeros are simple and lie on the line
. (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
DOI:
https://doi.org/10.1090/S0025-5718-1979-0537983-2
Keywords:
Gram blocks,
Riemann hypothesis,
Riemann zeta function,
Riemann-Siegel formula,
Rosser's rule,
Turing's theorem,
zeta functions
Article copyright:
© Copyright 1979
American Mathematical Society