Spectral parameter of Maass forms on PSL(2,Z[i]) (awaiting review)

Each Maass form is associated to an eigenvalue via the eigenvalue equation $(\Delta+\lambda)f(z)=0$ where $\Delta$ is the Laplacian. It is convenient to introduce the spectral parameter $r$ which is also called the eigenvalue. Only if one speaks about the true eigenvalue one refers to $\lambda$, since by convention eigenvalue refers to $r$. In hyperbolic 3-space, the eigenvalue is connected to the true eigenvalue via $\lambda=r^2+1$.

Keywords: #Maass #Picard