Fourier expansion of a Maass form on PSL(2,Z[i]) (awaiting review)

The Fourier expansion of a Maass forrm on PSL$(2,\Z[i])$ reads $$f(z)=\sum_{n\in\Z[i]}a(n)yK_{ir}(2\pi|n|y)e^{2\pi i\,\textrm{Re}(nx)},$$ where $K_{ir}(x)$ is a $K$-Bessel function and the expansion coefficients $a(n)$ are related to Hecke eigenvalues.

Keywords: #Maass #Picard