\(L\)-functions on \(GSp_2\times Gl_2\) of mixed weights
Let \(g\) be a holomorphic Siegel cusp form of degree 2 and weight \(k\) and let \(h\) be a holomorphic elliptic cusp form of weight \(l\) (\(k\) and \(l\) even, \(\geq 2\)). Assume \(g\) and \(h\) are Hecke eigenforms and the first Fourier-Jacobi coefficient of \(g\) is not identically zero. The authors prove the meromorphic continuation and functional equation of the \(L\)-function attached to \(g\) and \(h\). In case \(k=l\) this is contained in \textit{B. Heim} [Proc. Symp. Pure Math. 66, 201-238 (1999; Zbl 1001.11019)]. In the present paper differential operators are applied to one of the factors in the integrand of the integral representation of the \(L\)-function to obtain the result for arbitrary weights. The cases \(k\geq l\) and \(k<l\) demand different treatment.
scientific article; zbMATH DE number 1533431