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On integrality of Eisenstein liftings

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A Correction to this article was published on 01 December 1996

Abstract

Letf be a holomorphic Siegel modular form of integral weightk for Sp2r (Z). Forn≥r, let[f] nr 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 of[f] nr . 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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Authors and Affiliations

  1. Mathematisches Institut, Universität Heidelberg, Im Neuenheimerfeld 288, D 69120, Heidelberg, Germany

    Shin-ichiro Mizumoto

  2. Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, 152, Tokyo, Japan

    Shin-ichiro Mizumoto

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  1. Shin-ichiro Mizumoto
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Until July in 1996

An erratum to this article is available at http://dx.doi.org/10.1007/BF02568305.

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Mizumoto, Si. On integrality of Eisenstein liftings. Manuscripta Math 89, 203–235 (1996). https://doi.org/10.1007/BF02567514

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  • DOI: https://doi.org/10.1007/BF02567514

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