Timeline for Height of algebraic numbers
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 29, 2015 at 19:18 | review | Late answers | |||
| Sep 29, 2015 at 23:33 | |||||
| May 30, 2012 at 0:52 | comment | added | Joel Ouaknine | Thanks very much Kevin for the pointer. I just took Waldschmidt's book out and indeed it contains all the results I need! (By the way, your statement of Lemma 3.11 is missing an application of $\log(-)$ to $H(a)$ on both instances.) | |
| May 29, 2012 at 14:07 | comment | added | Kevin O'Bryant | This height is the "usual height", and is often written with a capital $H$ to distinguish it from the absolute logarithmic height. Waldschmidt (Lemma 3.11) reports $\frac1d H(a) - \log 2 \leq h(a) \leq \frac1d H(a) + \frac{1}{2d} \log(d+1)$, which can be combined with the bounds on other answers to bound $H(a+b)$ and $H(a/b)$. | |
| May 28, 2012 at 21:32 | comment | added | Joel Ouaknine | Thanks Will. I believe Oleg's height is the logarithmic Weil height, defined in terms of the Mahler measure. It is no doubt related to my "naive" height in some way, but I don't think it's simply the log of it. Or at least, it's far from obvious to me... | |
| May 28, 2012 at 21:05 | comment | added | Will Sawin | I think Oleg's height is the log of your height. | |
| May 28, 2012 at 19:51 | history | answered | Joel Ouaknine | CC BY-SA 3.0 |