On integrality of Eisenstein liftings |
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Authors: | Shin-ichiro Mizumoto |
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Institution: | 1. Mathematisches Institut, Universit?t Heidelberg, Im Neuenheimerfeld 288, D 69120, Heidelberg, Germany 2. Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, 152, Tokyo, Japan
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Abstract: | Letf be a holomorphic Siegel modular form of integral weightk for Sp2r (Z). Forn≥r, letf] r n be the lift off to Sp2n (Z) via the Klingen type Eisenstein series, which is defined under some conditions onk. We study an integrality property of the Fourier coefficients off] r n . A common denominator for them is described in terms of a critical value of the standardL-function attached tof, some Bernoulli numbers, and a certain ideal depending only onf. The result specialized to the caser=0 coincides with the Siegel-Böcherer theorem on the Siegel type Eisenstein series. |
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