ON INTEGRALITY OF EISENSTEIN LIFTINGS

Let f be a holomorphic Siegel modular form of integral weight k for Sp (2r)(Z). For n greater than or equal to r, let [f](n)(tau) be the lift of f to Sp(2n) (Z) via the Klingen type Eisenstein series, which is d efined under some conditions on k. We study an integrality property of the Fourier coefficients of [f](r)(n). A common denominator for them is described in terms of a critical value of the standard L-function a ttached to f, some Bernoulli numbers, and a certain ideal depending on ly on f. The result specialized to the case r = 0 coincides with the S iegel-Bocherer theorem on the Siegel type Eisenstein series.