Koecher–Maass series and certain kernel function associated to modular forms on the half-space of quaternions

In this paper, we first study analytic properties of Koecher–Maass series associated to Hermitian modular forms. Next, we define certain kernel function associated to Hermitian modular forms and modular forms on the half-space of quaternions and study their analytic properties. As an application, we derive another proof of analytic continuation and functional equation of the Koecher–Maass series associated to these modular forms.