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Results tagged with arithmetic-groups
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user 15629
18
votes
Accepted
Volumes of $\mathrm{SL}_n(K_\mathbb{R})/\mathrm{SL}_n(\mathcal{O}_K)$
$\DeclareMathOperator\SL{SL}$The same argument (due to Siegel, in a classical form, of course), adelized, gives the analogous computation for any number field, and, yes, the corresponding Dedekind zet …
- 23k
12
votes
Why are $S$-arithmetic groups interesting?
Supplementing other comments and @JimHumphreys' answer: Thinking of automorphic forms as living only on quotients of symmetric spaces or of real Lie groups leaves one with an extremely awkward neo-cla …
- 23k
2
votes
Accepted
Volume of arithmetic quotients of symmetric spaces
For a unimodular topological group $G$, and for discrete subgroups $\Theta\subset\Gamma\subset G$, for $f\in C^o_c(\Theta\backslash G)$, it is true that
$$
\int_{\Theta\backslash G} f \;=\; \int_{\Gam …
- 23k