Timeline for Question on effective Mordell conjecture
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Oct 26, 2014 at 15:27 | history | edited | Ariyan Javanpeykar | CC BY-SA 3.0 |
added extra paragraph
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| Oct 26, 2014 at 0:59 | comment | added | Vesselin Dimitrov | @zy_ : Neglecting the restriction on the genus, this is similar to asking for e.g. lower bounds on non-vanishing quantities of the form $|y^2 - x^3|$, $x,y \in \mathbb{Z}$. Baker's theory of logarithmic linear forms does yield a lower bound here of the shape $(\log{|x|})^{\kappa}$ for a small positive $\kappa > 0$, while the best possible statement $|y^2 - x^3| \gg_{\varepsilon} |x|^{\frac{1}{2}-\varepsilon}$ is a consequence of the ABC conjecture. Your general problem is a question about integral point on surfaces, and not much is known here (there has been some progress by Corvaja, Zannier). | |
| Oct 25, 2014 at 10:30 | comment | added | Y. Zhao | Thanks for your answer. Once I heard that rational points cannot lie very close to curves whose genus>1. Does abc conjecture give a conjectural lower bound? | |
| Oct 25, 2014 at 9:56 | history | answered | Ariyan Javanpeykar | CC BY-SA 3.0 |