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On the image of the Saito-Kurokawa lifting over a totally real number field and the Maass relation

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Abstract

We give a formula for the Fourier coefficients of the image of the Saito-Kurokawa lifting over a totally real number field \(K\), and we prove the image of the lifting satisfies a generalization of the Maass relation. We also give an explicit form of a Siegel series of degree 2 for any finite extension of \({\mathbb {Q}}_p\).

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Acknowledgments

The author would like to express his gratitude to Professor Tamotsu Ikeda for his encouragement and valuable advice.

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Authors and Affiliations

  1. Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan

    Atomu Otsuka

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  1. Atomu Otsuka
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Correspondence to Atomu Otsuka.

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Communicated by Ulf Kühn.

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Otsuka, A. On the image of the Saito-Kurokawa lifting over a totally real number field and the Maass relation. Abh. Math. Semin. Univ. Hambg. 84, 49–65 (2014). https://doi.org/10.1007/s12188-013-0086-y

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  • DOI: https://doi.org/10.1007/s12188-013-0086-y

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