Siegel series for skew Hermitian forms over quaternion algebras

Abstract

We prove a functional equation of Siegel series associated to nondegenerate semi-integral skew Hermitian forms over quaternion algebras over nonarchimedean local fields of characteristic not 2.

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Acknowledgments

The idea of the proof of Lemma 5.5 was suggested by Wee Teck Gan. We thank him for sharing his insight with us. The author is partially supported by JSPS Grant-in-Aid for Young Scientists (B) 26800017. This paper was written during the author’s stay at University of Rijeka. The author would like to thank the staffs of University of Rijeka, especially Neven Grbac, for an excellent working environment. We are grateful to the anonymous referee for a very careful reading and detailed comments, which helped improve the exposition of the earlier version.

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Correspondence to Shunsuke Yamana.

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Communicated by Jens Funke.

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Yamana, S. Siegel series for skew Hermitian forms over quaternion algebras. Abh. Math. Semin. Univ. Hambg. 87, 43–59 (2017). https://doi.org/10.1007/s12188-016-0127-4

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Keywords

  • Siegel series
  • Prehomogeneous vector spaces
  • Eisenstein series
  • Degenerate principal series
  • Quaternion algebras

Mathematics Subject Classification

  • 11E45
  • 11S90