A note on the Rankin-Selberg method for Siegel cusp forms of genus 2
\textit{W. Kohnen} and \textit{N.-P. Skoruppa} [Invent. Math. 95, 541-558 (1989; Zbl 0665.10019)] introduced a Dirichlet series \(D_{F,G}(s)\) associated with a pair of Siegel cusp forms \((F,G)\) of genus 2 and weight \(k\). It is defined by the Petersson scalar products of the Fourier-Jacobi coefficients of \(F\) and \(G\). If the first Fourier-Jacobi coefficient of \(F\) is not zero, then \(G\) can be chosen such that \(D_{F,G}(s)\) is proportional to the spinor zeta function of \(F\). In the paper under review the author applies these methods to the case that \(F\) and \(G\) are of level \(N\geq 1\).
scientific article; zbMATH DE number 1310587