Timeline for When is a Number Ring generated by its Norm-1 elements?
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 9, 2013 at 16:44 | comment | added | Gene S. Kopp | For a real quadratic field of discriminant $d$, the condition holds if and only if $\frac{d}{4}+1$ is a square, so, as you said, rarely. However, the relationship Bump mentions works for all real quadratic fields, if you phrase it as, "there's a natural bijection between the ideal classes of all orders $\mathcal{O}$ of $K$ and the hyperbolic conjugacy classes of ${\rm PSL}_2(\mathbb{Z})$ with eigenvalues in $K$." Your condition guarantees that the ideals of the max order $\mathcal{O}_K$ correspond to the conjugacy classes having the fundamental unit as an eigenvalue. | |
| Oct 2, 2013 at 22:12 | review | First posts | |||
| Oct 2, 2013 at 22:13 | |||||
| Oct 2, 2013 at 21:57 | history | asked | user38495 | CC BY-SA 3.0 |