Fourier–Jacobi expansion of automorphic forms on Sp(1,q) generating quaternionic discrete series

The aim of this paper is to develop the notion of the Fourier expansion of automorphic forms on Sp(1,q) generating quaternionic discrete series, which are non-holomorphic forms. There is such an expansion given by Tsuneo Arakawa, assuming the boundedness of the forms and the integrability of the discrete series. We study these automorphic forms without such assumptions. When q>1 we prove the “Koecher principle” for such automorphic forms, whose validity is known for holomorphic automorphic forms except elliptic modular forms.