Timeline for Unit in a number field with same absolute value at a real and a complex place
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Mar 12, 2010 at 10:06 | comment | added | Kevin Buzzard | I made an observation which I think solved the bonus question (take Filipe's solution, which is a product of two irreducible polys, with roots alpha,beta say, and then figure out the min polys of alpha(1+sqrt(2))^N and beta(1+sqrt(2))^N and multiply them together; for N suff large this will work), but was too lazy to do the algebra. | |
| Mar 12, 2010 at 3:33 | comment | added | Gerry Myerson | Since no one had posted an explicit solution to the bonus question I figured there must not be one and so there must be something wrong with my example - I must have missed some condition. I came up with several other "answers" before the one I posted only to realize that I had missed something in each of them. So I was hedging my bets. I'm glad my example passes muster. | |
| Mar 12, 2010 at 2:21 | comment | added | Felipe Voloch | That's a nice example and is better (lower degree) than what I could cook up following Kevin's suggestion, namely $f((1+\sqrt(2))x)f((1-\sqrt(2))x)$, where $f$ is the degree 12 polynomial in my original question. That solves the "bonus" but not the "strengthening" (which is just as well as per Ferguson) since your polynomial is reducible. Is that what you were referring to when you asked what were you missing? | |
| Mar 11, 2010 at 22:46 | history | answered | Gerry Myerson | CC BY-SA 2.5 |