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Inner product formula for Yoshida lifts

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Abstract

We prove an inner product formula for vector-valued Yoshida lifts by an explicit calculation of local zeta integrals in the Rallis inner product formula for \({\mathrm{O}}(4)\) and \({\mathrm {Sp}}(4)\). As a consequence, we obtain the non-vanishing of Yoshida lifts.

Résumé

Nous démontrons qu’une formule de produit scalaire pour relèvement de Yoshida valeurs vectorielles en un calcul explicite des intégrales de zêta locale dans la formule de produit scalaire de Rallis pour O(4) et Sp(4). En conséquence, nous obtenons le non-disparaition de relèvement de Yoshida.

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Acknowledgements

The authors would like to express their gratitude to Kazuki Morimoto for his careful reading and helpful comments. They also would like to thank the referee’s many valuable comments which improve the presentation of this paper. This work was done while the second author was a postdoctoral fellow in National Center for Theoretical Sciences in Taiwan. He is deeply grateful for their supports and hospitalities.

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Authors and Affiliations

  1. Institute of Mathematics, Academia Sinica, Taipei, 10617, Taiwan

    Ming-Lun Hsieh

  2. National Center for Theoretic Sciences, Hsinchu, Taiwan

    Ming-Lun Hsieh

  3. Department of Mathematics, School of Engineering, Tokyo Denki University, 5, Asahicho, Senju, Adachi City, Tokyo, 120-8551, Japan

    Kenichi Namikawa

Authors
  1. Ming-Lun Hsieh
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  2. Kenichi Namikawa
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Corresponding author

Correspondence to Kenichi Namikawa.

Additional information

Ming-Lun Hsieh was partially supported by MOST Grant 103-2115-M-002-012-MY5, and Kenichi Namikawa was supported by JSPS Grant-in-Aid for Research Activity Start-up Grant Number 15H06634 and Grant-in-Aid for Young Scientists (B) Grant Number 17K14174.

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Hsieh, ML., Namikawa, K. Inner product formula for Yoshida lifts. Ann. Math. Québec 42, 215–253 (2018). https://doi.org/10.1007/s40316-017-0088-8

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  • DOI: https://doi.org/10.1007/s40316-017-0088-8

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