It is well known that the first Kronecker limit theorem gives the Laurent expansion of the Eisenstein series $E(z,s)$ over $SL(2,Z)$ at $s=1$; see, for example, Serge Lang's book E …

I've heard that irreducible unitary representations of noncompact forms of simple Lie groups, the first example of such a group G being SL(2, R), can be completely described and th …

The decomposition of L^2(S^2) under SO(3; R) is well-known. Focus now on the hyperbolic plane H presented as the quotient SL(2; R)/SO(2; R). It is non-compact, therefore my under …