A **Maass form** of weight 0 on a subgroup \(\Gamma\) of \(\GL_{2}(\R)\)
is a smooth, square-integrable, automorphic eigenfunction of the Laplace-Beltrami operator $\Delta$. In other words,
$$f\in C^\infty(\mathcal{H}),\quad f\in L^2(\Gamma\backslash{\mathcal H}),\quad f(\gamma z)=f(z)\ \forall\gamma\in\Gamma,\quad (\Delta+\lambda)f(z)=0 \textrm{ for some } \lambda \in \C.$$

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- Review status: reviewed
- Last edited by Alex J. Best on 2018-12-19 06:36:23

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- 2018-12-19 06:36:23 by Alex J. Best (Reviewed)