Timeline for Hyperelliptic equation on a function field
Current License: CC BY-SA 4.0
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| Oct 1, 2020 at 18:37 | comment | added | Joe Silverman | > By the way, for g=1, is there some hope for a similar bound on a Mordell Weil generators set? Unfortunately, the answer is a resounding no. There's a conjecture (I think) that there exists a bound that's roughly exponentially worse than this. But I don't think that there are any theorems. (A good analogy is the Pell equation $x^2-Dy^2=1$, some of them have small'ish solutions, but presumably many of them have smallest solution that's exponential in $D$.) | |
| Oct 1, 2020 at 18:16 | comment | added | T. Combot | Thank you very much for your answer. Yes if you have a reference for the hyperelliptic result, such a bound seems very nice. By the way, for g=1, is there some hope for a similar bound on a Mordell Weil generators set? | |
| Oct 1, 2020 at 12:00 | history | answered | Joe Silverman | CC BY-SA 4.0 |