Timeline for Products of linear forms in 3 variables
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 1, 2010 at 14:06 | comment | added | Gerry Myerson | @lonekite, sorry, didn't occur to me to check the editing history. | |
| Sep 1, 2010 at 4:22 | comment | added | lonekite | @Gerry: Yes, I understand. Robin first gave an example of complex linear forms with the same property, then revised it using the cosine function. Anyway, both Robin's example and felix' are very helpful to me. Thank you all. | |
| Sep 1, 2010 at 0:32 | comment | added | Gerry Myerson | @lonekite, Robin's forms are linear. The cosine terms are numerical coefficients of the indeterminates $y$ and $z$. | |
| Aug 31, 2010 at 16:38 | history | edited | Robin Chapman | CC BY-SA 2.5 |
corrected detail; edited body
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| Aug 31, 2010 at 16:38 | comment | added | felix | Take any irreducible polynomial $f \in \mathbb{Q}[x]$ of degree 3 with real roots, say $\alpha, \beta, \gamma$. Set $f_1 = x + \alpha y + \alpha^2 z$, $f_2 = x + \beta y + \beta^2 z$, $f_3 = x + \gamma y + \gamma^2 z$. You can find plenty of polynomials <a href="cems.uvm.edu/~voight/nf-tables/3-25.txt">here</a>. | |
| Aug 31, 2010 at 16:33 | comment | added | lonekite | Could you give an explicit example or a reference? Thanks. | |
| Aug 31, 2010 at 16:27 | comment | added | Franz Lemmermeyer | Just take a totally real cubic field instead. Davenport studied such products a lot. | |
| Aug 31, 2010 at 16:18 | comment | added | lonekite | Sorry, but we are saying real linear forms... | |
| Aug 31, 2010 at 16:16 | history | answered | Robin Chapman | CC BY-SA 2.5 |