Fourier coefficients of generalized Eisenstein series of degree two. II (Q791567)

Let f be an elliptic cusp form of weight k with respect to \(Sl_ 2({\mathbb{Z}})\) and \([f](Z)=\sum_{T\geq 0}a(T) e^{2\pi i trace(TZ)}\) the associated Klingen-Eisenstein series of degree two. In Part I [Invent. Math. 65, 115-135 (1981; Zbl 0452.10032)] the author gave a formula for a(T) in the case that the discriminant of T is a fundamental discriminant and f is an eigenform of the Hecke algebra. In the paper under review this formula is generalized to arbitrary primitive \(T>0\) (theorem 1). From the formula rationality properties of those Fourier coefficients can be deduced (theorem 2). In theorem 3 it is shown that a(T)\(\neq 0\) for all binary quadratic forms \(T>0\), which represent 1 over \({\mathbb{Z}}\). - For generalizations of such explicit formulas to Eisenstein series of arbitrary degree one should consult the reviewer's paper [Math. Z. 183, 21-46 (1983; Zbl 0497.10020)].