Timeline for Extension of Tao-Green Theorem
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 1, 2011 at 20:08 | comment | added | Everett Piper | Is it the case, then, that $A_k$ has density roughly $1/\log^k N$ as well? Does the conjecture you're referring to cover $k>2$? My original interest in this problem was whether there could be a $k$ such that $\Sigma_{a\in A_k} 1/a$ could converge. I later learned of the conjecture of Erd\"os and the Green-Tao result. Do either of you have any insight into my original problem? | |
| Sep 27, 2011 at 7:55 | comment | added | Ben Green | I'm certain $A_1$ does contain long progressions, but proving it using the Tao-Green technique might not be so easy. In fact this set has density roughly $1/\log^2 N$ in the integers, and any such set is conjectured to have arbitrarily long progressions. | |
| Sep 27, 2011 at 6:20 | comment | added | Stefan Geschke | Yes, the set of primes with composite index has positive density in the set of all primes. Isn't this simply because the set of primes has density zero in the integers? | |
| Sep 27, 2011 at 3:18 | history | asked | Everett Piper | CC BY-SA 3.0 |