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A Converse Theorem for Split SO2l over Finite Fields

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Abstract

We prove a converse theorem for split even special orthogonal groups over finite fields. This is the only case left on converse theorems of classical groups and the difficulty is the existence of the outer automorphism. In this paper, we develop new ideas and overcome this difficulty.

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Acknowledgements

The authors would like to thank Professor Dihua Jiang and Professor Freydoon Shahidi for their interests and constant support. The authors also would like to thank Professor Qing Zhang for helpful communications.

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN, 47907, USA

    Alexander Hazeltine & Bai Ying Liu

Authors
  1. Alexander Hazeltine
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  2. Bai Ying Liu
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Correspondence to Bai Ying Liu.

Additional information

The research of the first-named author is partially supported by the NSF Grants DMS-1848058. The research of the second-named author is partially supported by the NSF Grants DMS-1702218, DMS-1848058, and by start-up funds from the Department of Mathematics at Purdue University

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Hazeltine, A., Liu, B.Y. A Converse Theorem for Split SO2l over Finite Fields. Acta. Math. Sin.-English Ser. 40, 731–771 (2024). https://doi.org/10.1007/s10114-023-2061-6

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  • DOI: https://doi.org/10.1007/s10114-023-2061-6

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