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The Eisenstein series for GL(3,Z) induced from cusp forms

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Abstract

We study the Eisenstein series for GL(3,Z) induced from cusp forms. We give the expression of the Fourier-Whittaker coefficients of the Eisenstein series in terms of the Jacquet integrals. Moreover, by evaluating the Jacquet integrals, we give the Mellin-Barnes type integral expressions of those at the minimal K-type.

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Acknowledgements

The author would like to express his gratitude to Professor Takayuki Oda for valuable advice on this work, and also thanks to Kazuki Hiroe for correction of the first draft.

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  1. Department of Mathematics, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima-ku, Tokyo, 171-8501, Japan

    Tadashi Miyazaki

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  1. Tadashi Miyazaki
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Correspondence to Tadashi Miyazaki.

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Communicated by U. Kühn.

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Miyazaki, T. The Eisenstein series for GL(3,Z) induced from cusp forms. Abh. Math. Semin. Univ. Hambg. 82, 1–41 (2012). https://doi.org/10.1007/s12188-012-0064-9

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  • DOI: https://doi.org/10.1007/s12188-012-0064-9

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