Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
MathSciNet review: 537983
Full-text PDF Free Access

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 = \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} $. (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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 10H05

Retrieve articles in all journals with MSC: 10H05


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1979-0537983-2
PII: S 0025-5718(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