On Siegel series for Hermitian forms. II (Q1113931)

The author calculates the Fourier coefficients of the Siegel-Eisenstein series (related with the Gaussian number field) of weight k on the Hermitian half-space of degree 2. If \(k\geq 4\), \(k\equiv 0 mod 4\), the Fourier coefficient of a half-integral positive definite matrix H equals \(\rho_ k(\det H)^{k-2} b(k,H),\) where \(\rho_ k\) denotes an explicitly given constant and b(k,H) the attached Siegel series, which was already computed by the author in Part I [Proc. Japan Acad., Ser. A 63, 73-75 (1987; Zbl 0626.10025)]. In the case \(k=4\) the Eisenstein series is defined by Hecke's trick and coincides with the theta series attached to Iyanaga's form.