Answer by Lee Mosher for Conjugacy classes of $\mathrm{SL}_2(\mathbb{Z})$
One can proceed as follows for $SL_2(\mathbb{Z})$.First, the trace is a conjugacy invariant.For trace $0$ there are two conjugacy classes represented by $\pmatrix{0 & 1 \\ -1 & 0}$ and...
View ArticleAnswer by Stefan Kohl for Conjugacy classes of $\mathrm{SL}_2(\mathbb{Z})$
The conjugacy classes of elements of ${\rm SL}(2,\mathbb{Z})$with given trace are counted in:S. Chowla, J. Cowles and M. Cowles:On the number of conjugacy classes in SL(2,Z). Journal of Number Theory...
View ArticleAnswer by Igor Rivin for Conjugacy classes of $\mathrm{SL}_2(\mathbb{Z})$
This is the subject of Gauss' reduction theory, as discussed in Karpenkov's book (among many other places). In this 2007 paper, Karpenkov also extends the method to $SL(n, \mathbb{Z}).$
View ArticleConjugacy classes of $\mathrm{SL}_2(\mathbb{Z})$
I was wondering if there is some description known for the conjugacy classes of $$\mathrm{SL}_2(\mathbb{Z})=\{A\in \mathrm{GL}_2(\mathbb{Z})|\;\;|\det(A)|=1\}.$$ I was not able to find anything about...
View Article
