Geodesic
Analytic properties of the convolution of Siegel modular forms of genus~$n$
Sbornik. Mathematics, Tome 48 (1984) no. 1, pp. 193-200

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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. 
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     author = {V. L. Kalinin},
     title = {Analytic properties of the convolution of {Siegel} modular forms of genus~$n$},
     journal = {Sbornik. Mathematics},
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     url = {http://geodesic.mathdoc.fr/item/SM_1984_48_1_a10/}
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V. L. Kalinin. Analytic properties of the convolution of Siegel modular forms of genus~$n$. Sbornik. Mathematics, Tome 48 (1984) no. 1, pp. 193-200. http://geodesic.mathdoc.fr/item/SM_1984_48_1_a10/