Timeline for Largest observed value of $S(t)$
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 13, 2019 at 11:02 | comment | added | Farzad Aryan | Thanks for the info. | |
| Nov 12, 2019 at 10:07 | comment | added | MyNinthAccount | Also, they indicate that Sarnak's 3.2 in 2004 wasn't really known? "Nevertheless, previous to these computations, the largest observed value of $S(t)$ seems to have been $−2.9076$, as reported by Gourdon [8]. Table 2 lists 11 spots where we have found values of $|S(t)| > 3.1$, the largest of which is $S(t) ≈ 3.3455$ for $t ≈ 7.75×10^{27}$. " | |
| Nov 12, 2019 at 10:05 | comment | added | MyNinthAccount | Bober & Hiary, 2016: This resulted in the largest computed value of $Z(t) ≈ 16244.8652$ and $S(t) ≈ 3.3455$. research-information.bristol.ac.uk/files/86475229/zetaComp.pdf | |
| Nov 11, 2019 at 17:30 | comment | added | Lucia | No, how can it -- it is numerical evidence. But the numerical evidence does not at all indicate the Alternative Hypothesis. The only reason we think about the Alternative Hypothesis is that it is related to the Siegel zero problem. | |
| Nov 11, 2019 at 17:21 | comment | added | Farzad Aryan | Does the work of Odlyzko's reject the AGUE (say in its mild form, that almost all spacing are half integers)? Given that the Alternative Hypothesis is compatible with what is currently known about the pair correlation of the zeros of zeta. | |
| Nov 11, 2019 at 15:55 | comment | added | Lucia | Odlyzko's computations on the nearest neighbour spacings match the GUE predictions extremely closely. There is a huge difference between GUE and AGUE as far as the nearest neighbour spacings go -- AGUE would have spacings quantised at half-integer values of the usual spacing. One simply does not see that. Large values of $S(t)$ probably grow like $\sqrt{\log T \log \log T}$ --- you are unlikely to see large values. I would write to Jonathan Bober or Ghaith Hiary for the current numerical data. | |
| Nov 11, 2019 at 14:13 | history | asked | Farzad Aryan | CC BY-SA 4.0 |