Timeline for Lower bound on number of smooth values of polynomial at primes
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Nov 2, 2014 at 21:48 | comment | added | Terry Tao | For what it's worth: there is at least one error in the proof of Lemma 2 in the arXiv preprint, namely in the third line of (21). An equality of integers is claimed there due to (18), but (18) only gives the claimed equality modulo $p^{i-1}(p-1)$. This is insufficient to then deduce the next line of (21). | |
| Nov 2, 2014 at 21:06 | comment | added | Terry Tao | Standard heuristics would suggest that this proportion should be $\rho(d/u)$, where $d$ is the degree of $f$ and $\rho$ is Dickman's function. So, the claimed lemma should fail about $\rho(11) \approx 10^{-12}$ of the time, suggesting that counterexamples exist but would require an immense amount of computation to locate numerically. | |
| Nov 2, 2014 at 20:07 | comment | added | Dror Speiser | I overshot there a bit... :) | |
| Nov 2, 2014 at 20:06 | history | edited | Dror Speiser | CC BY-SA 3.0 |
changed wording to suit current knowledge/beliefs
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| Nov 2, 2014 at 19:46 | comment | added | Lucia | I don't think we know that values of polynomials get smooth (except for $u$ in some limited range), let alone for polynomials evaluated at primes. | |
| Nov 2, 2014 at 18:39 | history | asked | Dror Speiser | CC BY-SA 3.0 |