On certain L-series of Rankin-Selberg type associated to Siegel modular forms of degree 2

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We study certain L-series of Rankin-Selberg type associated to Siegel modular forms of degree 2: twists by Dirichlet characters, relation to zeta functions of spinor type, construction of Siegel cusp forms whose Fourier coefficients involve special values of such L-series, etc.