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Bessel identities in the Waldspurger correspondence over the complex numbers

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Abstract

We prove certain identities between relative Bessel functions attached to irreducible unitary representations of PGL2(ℂ) and Bessel functions attached to irreducible unitary representations of SL2(ℂ). These identities reflect the Waldspurger correspondence over ℂ. We also prove several regularity theorems for Bessel and relative Bessel distributions which appear in the relative trace formula. This paper constitutes the local spectral theory of Jacquet’s relative trace formula over ℂ.

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Authors and Affiliations

  1. School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China

    Jingsong Chai

  2. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China

    Zhi Qi

Authors
  1. Jingsong Chai
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  2. Zhi Qi
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Corresponding author

Correspondence to Zhi Qi.

Additional information

The first author is supported by the National Natural Science Foundation of China [Grant 11771131].

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Chai, J., Qi, Z. Bessel identities in the Waldspurger correspondence over the complex numbers. Isr. J. Math. 235, 439–463 (2020). https://doi.org/10.1007/s11856-020-1966-3

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  • DOI: https://doi.org/10.1007/s11856-020-1966-3

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