6
votes
0answers
120 views

Phillips-Sarnak conjecture in higher dimension

The Phillips-Sarnak conjecture states that for a generic Fuchsian lattice the space of Maass cusp forms is finite-dimensional. Generic here means in particular non-uniform, non-arithmetic, no special ...
3
votes
1answer
263 views

Weyl law for SL(2,C)

Are there any estimates for the eigenvalues of the Laplace operator for $\Gamma \backslash SL(2, \mathbb{C})/SU(2)$ known beyond the main term? Here, $\Gamma$ should be congruence subgroup in ...
4
votes
1answer
606 views

Why is the cuspidal spectrum discrete?

Hi, I have a short question concerning the spectral theory of automorphic forms. What is the main property of the unipotent group $N$, which consist of matrices in the form ...
4
votes
0answers
241 views

spectral decomposition for elliptic surfaces?

I'm looking for explicit formulae for the spectral decomposition of $L^2(S)$, where $S$ is an elliptic surface (of complex dimension 2). To be precise, the elliptic surface I'm looking at is the ...