Koecher-Maass series associated to Hermitian modular forms of degree 2 and a characterization of cusp forms by the Hecke bound

Abstract

We establish basic analytic properties of the Koecher-Maass series associated to Hermitian modular forms of degree 2, level N, twisted by Maass forms on 3-dimensional hyperbolic space. As one of its applications, we give a characterization of degree 2 Hermitian cusp forms by the growth of their Fourier coefficients.