Timeline for Random Diophantine polynomials: Percent solvable?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 27, 2015 at 12:21 | comment | added | Joseph O'Rourke | Thanks, quid. Your calculations are remarkably accurate. Nice analysis. | |
| Apr 27, 2015 at 12:18 | comment | added | user9072 | @JosephO'Rourke the problem of estimating this is known as Dirichlet divisor problem and there are better estimates than what I gave. See mathworld.wolfram.com/DirichletDivisorProblem.html for an overview. I think the extual error term should be only slightly larger than a fourth root of $C$, what is known is order $C^a$ with $a=131/416$. I do not know right now what is known regarding the implied constants. For the weak error term I give $6$ would work IIRC. | |
| Apr 27, 2015 at 12:00 | comment | added | Joseph O'Rourke | Another data point for $C=50$: $9.1$%. Your formulas predict about $9.2$%. May I ask: What are you estimating for the $O(\sqrt{C})$ term? | |
| Apr 27, 2015 at 8:57 | comment | added | user9072 | I changed the notation in a different way to make clear that indeed this is the intent. Thanks for pointing out the confusing notation. | |
| Apr 27, 2015 at 8:55 | history | edited | user9072 | CC BY-SA 3.0 |
changed notation on comment
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| Apr 27, 2015 at 8:07 | comment | added | user5810 | Presumably $\: \log C/C \:$ should be replaced with $\: (\log C)/C \;$. $\;\;\;\;$ | |
| Apr 27, 2015 at 0:36 | history | answered | user9072 | CC BY-SA 3.0 |