Maass forms

introduction

Hyperbolic distribution problems and half-integral weight Maass forms
Automorphic forms correspond to representations that occur in $L_2(\Gamma\backslash G)$.
In the case when $G$ is $SL_2$
- holomorphic modular forms correspond to (highest weight vectors of) discrete series representations of $G$
- Maass wave forms correspond to (spherical vectors of) continuous series representations of G.

Henryk Iwaniek, Emmanuel Kowalski (2004). Analytic number theory
Lectures on modular functions of one complex variable (Tata Institute of Fundamental Research. Lectures on mathematics and physics. Mathematics, 29)
- Hans Maass, (pdf)