Timeline for Upper bound on answer for Pell equation
Current License: CC BY-SA 3.0
4 events
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| Jan 28, 2016 at 2:50 | comment | added | Joe Silverman | @Lucia I stated Siegel's theorem precisely and then prefaced the rest of the post with "at least approximately." The poster is looking at experimental data, so rather than guessing a bound of $p^{\sqrt p}$, he'd be better off first trying to estimate the growth rate of the upper bound for $\log|x_0|$, which would hide some of the lower order phenomena. Then, as you say, one should be able to guess $\gg\ll p^{1/2\pm\epsilon}$. Following Siegel blindly and pretending lower order terms don't exist gives what I wrote; I made no claim it was accurate. Thanks for being more precise. | |
| Jan 27, 2016 at 23:28 | comment | added | Lucia | You only get from this a bound of $\exp(p^{1/2+\epsilon})$. Please see argument in my answer below. | |
| Jan 27, 2016 at 21:52 | vote | accept | Will Jagy | ||
| Jan 27, 2016 at 23:55 | |||||
| Jan 27, 2016 at 21:39 | history | answered | Joe Silverman | CC BY-SA 3.0 |