Timeline for Upper bound on number of integral solutions of elliptic curves
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 10, 2023 at 9:58 | comment | added | Navvye | @ChrisWuthrich Thank you for your comment - I'm not looking at a specific example however, i'm looking at the general class of mordell equations | |
| Nov 10, 2023 at 9:29 | comment | added | Chris Wuthrich | For a specific example, you can do much better in practice. Look at Nigel Smart's "The algorithmic resolution of diophantine equations." Chapter VII.4, or other suggestions given in these answers | |
| Nov 10, 2023 at 8:36 | comment | added | Navvye | Yes, I need to know the explicit bound $C$ in order to do some computations about specific solutions to Mordell Equations. If I have to find the constant, how would I go about doing it? Also, what evidence points to $C$ being effectively computable? I know it doesn't depend upon Roth's theorem, which is a good sign.. | |
| Nov 10, 2023 at 6:30 | comment | added | Stanley Yao Xiao | @Navvye what you are asking for is for an explicit bound on $C = C(\varepsilon)$. It seems that the methods used to prove the theorems in that paper are effective, so in principle such a bound can be deduced. However, the authors have made no effort to compute the implied constant, and for someone else to do so is a major task, having to trace through not only the arguments in that paper but also the cited papers. Is there any specific application you have in mind that would require such precision, or do you just need to know that $C$ is effectively computable? | |
| Nov 10, 2023 at 5:05 | comment | added | Navvye | I've edited the original question to reflect the change in the question if that's alright | |
| Nov 10, 2023 at 0:56 | comment | added | Stanley Yao Xiao | @Navvye It seems you are asking a different question in the above comment. If so, please ask a new question. I believe Bogdan has given you a satisfactory answer to your original question, which means that you should accept his answer (after a few days to see if someone can give you a more insightful answer, but I doubt that's possible within the scope of the original question). | |
| Nov 9, 2023 at 21:49 | comment | added | Navvye | Thank you so much. How exactly should I decide which $C$ to use? Is this related to Hall's conjecture? | |
| Nov 9, 2023 at 18:55 | history | answered | Bogdan Grechuk | CC BY-SA 4.0 |