Timeline for Small quotients of smooth numbers
Current License: CC BY-SA 3.0
23 events
| when toggle format | what | by | license | comment | |
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| S Jan 21, 2016 at 15:00 | history | bounty ended | CommunityBot | ||
| S Jan 21, 2016 at 15:00 | history | notice removed | CommunityBot | ||
| Jan 15, 2016 at 16:02 | answer | added | Basj | timeline score: 1 | |
| Jan 14, 2016 at 8:52 | history | edited | Kurisuto Asutora | CC BY-SA 3.0 |
added 192 characters in body
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| Jan 14, 2016 at 8:44 | answer | added | Christian Elsholtz | timeline score: 2 | |
| S Jan 13, 2016 at 13:56 | history | bounty started | Kurisuto Asutora | ||
| S Jan 13, 2016 at 13:56 | history | notice added | Kurisuto Asutora | Draw attention | |
| S Dec 1, 2015 at 13:54 | history | bounty ended | CommunityBot | ||
| S Dec 1, 2015 at 13:54 | history | notice removed | CommunityBot | ||
| Nov 26, 2015 at 2:46 | answer | added | Noam D. Elkies | timeline score: 8 | |
| Nov 24, 2015 at 13:22 | comment | added | Kurisuto Asutora | I tried to activate this post again, since the problem is still unsolved. It would be already sufficient to get an upper bound for the quotient in the first displayed equation if a "small" number of exceptional pairs $\ell_1, \ell_2$ can be excluded. "Small" here means something smaller than any fixed power of $N$, or preferably even less. | |
| S Nov 23, 2015 at 12:07 | history | bounty started | Kurisuto Asutora | ||
| S Nov 23, 2015 at 12:07 | history | notice added | Kurisuto Asutora | Draw attention | |
| Apr 28, 2015 at 19:11 | answer | added | Gerhard Paseman | timeline score: 1 | |
| Apr 21, 2015 at 11:47 | comment | added | Kurisuto Asutora | Hi Lucia, thanks for your remark. Yes, I also think that this is very interesting. The problem arises in my work when trying to control the mean value of certain Dirichlet series (or, more precisely, of the mean value of the squared absolute value of certain finite Euler products), but I think it is of some interest on its own right. | |
| S Apr 21, 2015 at 10:03 | history | bounty ended | CommunityBot | ||
| S Apr 21, 2015 at 10:03 | history | notice removed | CommunityBot | ||
| Apr 20, 2015 at 5:10 | comment | added | Lucia | I think this is a very interesting question, and don't believe it is known. Note that it implies your other question on logarithms of ratios of square-free numbers, which also is unknown I think. Finally, it may be worth pointing out that the kind of bound you are asking for is best possible -- random products of the first $k$ primes will cluster, and then use pigeonhole to find two near each other. | |
| S Apr 13, 2015 at 8:07 | history | bounty started | Kurisuto Asutora | ||
| S Apr 13, 2015 at 8:07 | history | notice added | Kurisuto Asutora | Draw attention | |
| Apr 13, 2015 at 8:02 | history | edited | Kurisuto Asutora | CC BY-SA 3.0 |
added 36 characters in body
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| Apr 8, 2015 at 15:59 | comment | added | The Masked Avenger | Using the symmetry d goes to $n_N$/d, you can improve the lower bound by dividing the exponent by 2, as well as getting an upper bound by averaging over the interval $(k, N_n^{1/2})$. With examples like 715/714, it may be that you can't remove log k from the exponent. | |
| Apr 8, 2015 at 9:06 | history | asked | Kurisuto Asutora | CC BY-SA 3.0 |