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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 12th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to * R. P. Brent, J. van de Lune, H. J. J. te Riele and D. T. Winter, _On the Zeros of the Riemann Zeta Function in the Critical Strip. II_, Mathematics of Computation Mathematics of Computation Vol. 39, No. 160 (Oct., 1982), pp. 681-688 ([doi:10.2307/2007345 ](https://www.jstor.org/stable/2007345)) for computer-checks of the Riemann hypothesis. (there are probably more recent such?) <a href="https://ncatlab.org/nlab/revision/diff/Riemann+hypothesis/8">diff</a>, <a href="https://ncatlab.org/nlab/revision/Riemann+hypothesis/8">v8</a>, <a href="https://ncatlab.org/nlab/show/Riemann+hypothesis">current</a>

   added pointer to

   • R. P. Brent, J. van de Lune, H. J. J. te Riele and D. T. Winter, On the Zeros of the Riemann Zeta Function in the Critical Strip. II, Mathematics of Computation Mathematics of Computation Vol. 39, No. 160 (Oct., 1982), pp. 681-688 (doi:10.2307/2007345 )

   for computer-checks of the Riemann hypothesis. (there are probably more recent such?)

   diff, v8, current

2. • CommentRowNumber2.
   • CommentAuthorDavidRoberts
   • CommentTimeNov 12th 2018
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexI would check the references to Helfgott's proof of the weak Goldbach conjecture, the small end of which relied on verified computations of zeta zeroes. In particular, there was work of Platt (possibly joint) that was cited.

   I would check the references to Helfgott’s proof of the weak Goldbach conjecture, the small end of which relied on verified computations of zeta zeroes. In particular, there was work of Platt (possibly joint) that was cited.

3. • CommentRowNumber3.
   • CommentAuthorDavidRoberts
   • CommentTimeNov 12th 2018
   • (edited Nov 12th 2018)
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexEven better: see links [here on Terry Tao's blog](https://terrytao.wordpress.com/2018/09/06/polymath15-tenth-thread-numerics-update/): - [Platt](https://doi.org/10.1090/mcom/3198) - [Gourdon](http://numbers.computation.free.fr/Constants/Miscellaneous/zetazeros1e13-1e24.pdf)

   Even better: see links here on Terry Tao’s blog:

   • Platt
   • Gourdon
4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeNov 12th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks! Have added the pointers [here](https://ncatlab.org/nlab/show/Riemann+hypothesis#ReferencesComputerChecks).

   Thanks! Have added the pointers here.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeDec 29th 2018
   • (edited Dec 29th 2018)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded one more item in the list of references for computer-checks of zeroes of the Riemann zeta function: * A. M. Odlyzko, _The $10^{22}$-nd zero of the Riemann zeta function_, in Lapidus et al. (eds.) proceedings of AMS special session on _Dynamical, Spectral, and Arithmetic Zeta Functions_, 1999 ([pdf](http://www.dtc.umn.edu/~odlyzko/doc/zeta.10to22.pdf)) <a href="https://ncatlab.org/nlab/revision/diff/Riemann+hypothesis/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/Riemann+hypothesis/10">v10</a>, <a href="https://ncatlab.org/nlab/show/Riemann+hypothesis">current</a>

   added one more item in the list of references for computer-checks of zeroes of the Riemann zeta function:

   • A. M. Odlyzko, The $10^{22}$-nd zero of the Riemann zeta function, in Lapidus et al. (eds.) proceedings of AMS special session on Dynamical, Spectral, and Arithmetic Zeta Functions, 1999 (pdf)

   diff, v10, current