Timeline for Approaches to Riemann hypothesis using methods outside number theory
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 22, 2010 at 13:46 | comment | added | Andrea Mori | Well, when I first learned of the Weil-Shimura-Taniyama conjecture (that was about the time Fermat's last theorem was reduced to it) nobody an idea on how to attack it "reasonably" | |
| Aug 7, 2010 at 2:45 | comment | added | Junkie | Yes, I thought of E/H last night. Goldston/Yildirim again "comes close" to twin primes (or at least bounded gaps) in some metrical sense, but the sqrt bound on moduli is a huge barrier for Bombieri-Vinogradov (it can be crossed in very stringent circumstances, but these are not easy to enhance), so again I'm not sure it is real progress as I would like it. I could think to rephrase this: many ideas of attacking twin primes have yielded some partial results, but turn out to fall short in the end, and in some cases have exemplified what the deeper matter is (parity problem, sqrt bound). | |
| Aug 6, 2010 at 23:24 | comment | added | David Hansen | @Junkie: One potential yardstick for progress towards twin primes might be any progress towards the Elliott-Halberstam conjecture, of which there has been very little indeed. | |
| Aug 6, 2010 at 9:34 | comment | added | Junkie | I can't name one progress toward twin primes, that has a chance of working to prove it. I was excited about Friedlander/Iwaniec and $X^2+Y^4$ for awhile, as it critically broke the parity problem, but it can't handle sparse enough sequences. Upper bounds are similar to density estimates on zeros -- simply what the technology can currently spit out. Chen's theorem is another mild chip, maybe somewhat like a zero-free region. None are close to twin primes. I might even argue the other way around, that the minimal progress toward RH is more significant, particularly the function field analogue. | |
| Aug 6, 2010 at 3:20 | comment | added | Micah Milinovich | For the most part I agree with you, but I think the progress made toward twin primes is much more significant. | |
| Aug 6, 2010 at 1:53 | comment | added | Junkie | I think twin primes is essentially the same. There's a lot of flotsam around both of them (like partial results with sieves, or density estimates on zeros), but none of it reaches the core of what is really going on for a proof of the desired result. | |
| Aug 6, 2010 at 1:08 | history | answered | Micah Milinovich | CC BY-SA 2.5 |