Timeline for Relations among the height of algebraic numbers
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 29, 2014 at 19:33 | comment | added | Diego Marques | Unfortunately, I have no Waldschmidt book with the relations between H(a) and h(a) (weyl height). With the estimates given in Zieve link I got H(a-b)<< H(a)^H(b) or something like that. | |
| Jun 29, 2014 at 12:05 | comment | added | Joe Silverman | You can get such an estimate for the $d$'th root of the largest coefficient, where $d$ is the degree of the minimal poly. There are standard estimates relating the usual height $H_1(a)$ (not your quantity) and $H_2(a)$ the $d$'th root your height. (See the answers to the question that Michael Zieve gives the link.) For $H_1$, one has (if I remember correctly) $H_1(a-b)\le2H_1(a)H_1(b)$. From this one can get a similar estimate for $H_2$. | |
| Jun 29, 2014 at 5:59 | comment | added | Michael Zieve | Related question: mathoverflow.net/questions/64643/… | |
| Jun 29, 2014 at 5:49 | comment | added | Michael Zieve | This is not possible unless you bound the degrees of a and b as well. The trace of $a+1$ is $\text{tr}(a)+\text{deg}(a)$. | |
| Jun 29, 2014 at 4:36 | review | First posts | |||
| Jun 29, 2014 at 7:38 | |||||
| Jun 29, 2014 at 4:16 | history | asked | Diego Marques | CC BY-SA 3.0 |