Steinberg representation of GSp(4): Bessel models and integral representation of L-functions

@article{Pitale2009SteinbergRO,
  title={Steinberg representation of GSp(4): Bessel models and integral representation of L-functions},
  author={Ameya Pitale},
  journal={Pacific Journal of Mathematics},
  year={2009},
  volume={250},
  pages={365-406}
}
  • Ameya Pitale
  • Published 23 September 2009
  • Mathematics
  • Pacific Journal of Mathematics
We obtain explicit formulas for the test vector in the Bessel model, and derive the criteria for existence and uniqueness of Bessel models for the unramified quadratic twists of the Steinberg representation π of GSp 4 (F), where F is a nonarchimedean local field of characteristic zero. We also give precise criteria for the Iwahori spherical vector in π to be a test vector. We apply the formulas for the test vector to obtain an integral representation of the local L-function of π, twisted by any… 
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