Timeline for Heights of multiples of rational points on elliptic curves
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 15, 2016 at 12:59 | vote | accept | WhatsUp | ||
| May 13, 2016 at 0:24 | answer | added | Joe Silverman | timeline score: 5 | |
| May 12, 2016 at 23:05 | comment | added | WhatsUp | @ACL You are right. I just figured it out myself. Do you have idea for the denominator? | |
| May 12, 2016 at 23:01 | comment | added | ACL | There is a uniform bound for $h(P)-\hat h(P)$; apply it to the point nP and use that $\hat h(nP)=n^2\hat h(P)$. | |
| May 12, 2016 at 22:55 | comment | added | WhatsUp | @ACL Could you tell me where in the book of Silverman is this result stated? The canonical height, by definition, is the limit of $h(2^n P)/4^n$, which is different from what you write. Besides, his Corollary 6.4 of Chapter VIII has a big O constant that depends on $m$. | |
| May 12, 2016 at 22:43 | comment | added | ACL | The answer to the second question is YES, and is certainly explained in books on elliptic curves such as Joe Silverman's : the canonical height of $P$, $\hat h(P)$, is the limit of $h(x(nP))/n^2$, when $n\to\infty$. | |
| May 12, 2016 at 22:21 | history | asked | WhatsUp | CC BY-SA 3.0 |