Timeline for 4-distance problem and elliptic curves
Current License: CC BY-SA 4.0
15 events
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Mar 16, 2022 at 21:22 | history | edited | Yuan Yang | CC BY-SA 4.0 |
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Mar 16, 2022 at 13:47 | history | edited | Yuan Yang | CC BY-SA 4.0 |
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Mar 16, 2022 at 12:13 | history | edited | Yuan Yang | CC BY-SA 4.0 |
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Mar 16, 2022 at 12:12 | comment | added | Yuan Yang | @JoachimKönig You are so right, thank you so much for pointing out! | |
Mar 16, 2022 at 12:10 | comment | added | Joachim König | @YuanYang With the corrected coefficients, Magma says $r=1/8$ is a counterexample. | |
Mar 16, 2022 at 12:01 | comment | added | Will Sawin | @StanleyYaoXiao Couldn't a disproof consist of a single counerexample? I agree proving the proportion where at least one has rank $0$ is exactly $75\%$ is beyond current technology. | |
Mar 16, 2022 at 12:00 | comment | added | Gerry Myerson | This is D19 in Guy, Unsolved Problems In Number Theory, where there is a discussion and loads of references to the literature. Worth a look, if you are interested in the problem and haven't already seen Guy's book. | |
Mar 16, 2022 at 11:57 | comment | added | Yuan Yang | @JoachimKönig Ahhh thank you for pointing out! I had a typo it should be $-2/r^2 x+1/r^2$ | |
Mar 16, 2022 at 11:56 | history | edited | Yuan Yang | CC BY-SA 4.0 |
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Mar 16, 2022 at 11:54 | comment | added | Joachim König | @YuanYang: No, I mean the way the constant coefficient is currently written as $-2/r^2+1/r^2$, it looks like a typo (and also computation doesn't show what you claim with this form). | |
Mar 16, 2022 at 11:53 | comment | added | Chris Wuthrich | Related : mathoverflow.net/questions/301991/four-distance-problem | |
Mar 16, 2022 at 11:51 | comment | added | Yuan Yang | @JoachimKönig when $r=0$ it’s a degenerate case; the relation of $r$ and $1-r$ is crucial so I stayed this form | |
Mar 16, 2022 at 11:45 | comment | added | Joachim König | Is there a mistake in the constant coefficient of your family (or possibly $x$ missing for the linear term) ? | |
Mar 16, 2022 at 11:40 | comment | added | Stanley Yao Xiao | Given general conjectures about ranks of elliptic curves your conjecture is likely false. The amount of computational evidence you provided to support your conjecture is paltry at best. Regardless, either a proof or disproof of your conjecture for all $r$ is likely beyond current technology. | |
Mar 16, 2022 at 11:25 | history | asked | Yuan Yang | CC BY-SA 4.0 |