Nonvanishing of Koecher–Maass series attached to Siegel cusp forms

We prove a nonvanishing result for Koecher–Maass series attached to Siegel cusp forms of weight k and degree n   in certain strips on the complex plane. When n=2n=2, we prove such a result for forms orthogonal to the space of the Saito–Kurokawa lifts ‘up to finitely many exceptions’, in bounded regions.