Analytic properties of the convolution of Siegel modular forms of genus $n$

It is shown that the Rankin convolution of two Siegel modular forms (of which at least one is a cusp form) extends meromorphically onto the whole complex plane. In the case of the full modular group of genus $n$, the singularities of the Rankin convolution are studied to within a finite number of points, and functional equations are obtained. By means of a Tauberian theorem, a limiting relation is obtained for the weighted sum of the squares of the Fourier coefficients of a cusp form.
Bibliography: 5 titles.