Timeline for Numerical Evidence for Grand Riemann Hypothesis?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 13, 2017 at 10:43 | comment | added | post.as.a.guest | I thought the entire Rubinstein FRG (2008-12) was supposed to produce (literally) trillions of zeros of L-functions of all sorts of degrees. "We will test the Generalized Riemann Hypothesis for millions of L-functions of degrees 1,2,3,4 to large height: on the order of $10^{13}$ zeros will be computed for degree 1, $10^{10}$ zeros for degree 2, $10^8$ zeros for degree 3, and $10^7$ zeros for degree 4." What happened in the end? I'm not getting anything from his Waterloo website currently. If the LMFDB data has this, it is somewhat hidden. E.g., 11a has zeros up to height only 20? | |
| Mar 13, 2017 at 3:32 | comment | added | Felipe Voloch | Lots of data at lmfdb.org | |
| Mar 13, 2017 at 3:31 | comment | added | KConrad | Maybe not "giant number," but GRH for $L(s,\tau)$ has been numerically tested. See H. Yoshida, "On calculations of zeros of $L$-functions related with Ramanujan's discriminant function on the critical line," J. Ramanujan Math. Soc. 3 (1988), no. 1, 87–95. (On MathSciNet it is MR0975839 (90b:11044)). | |
| Mar 12, 2017 at 22:35 | comment | added | GH from MO | I think there have been numerical experiments with $\mathrm{GL}_2$ and $\mathrm{GL}_3$ cusp forms (Rubinstein, Farmer, Booker etc.). | |
| Mar 12, 2017 at 19:57 | history | asked | 7-adic | CC BY-SA 3.0 |