On counting cuspidal automorphic representations for $\mathrm{GSp}(4)$

M. Roy; R. Schmidt; Shaoyun Yi

Corpus ID: 224802986

On counting cuspidal automorphic representations for $\mathrm{GSp}(4)$

@article{Roy2020OnCC,
  title={On counting cuspidal automorphic representations for \$\mathrm\{GSp\}(4)\$},
  author={M. Roy and R. Schmidt and Shaoyun Yi},
  journal={arXiv: Number Theory},
  year={2020}
}

M. Roy, R. Schmidt, Shaoyun Yi

Published 2020

Mathematics

arXiv: Number Theory

We find the number $s_k(p,\Omega)$ of cuspidal automorphic representations of $\mathrm{GSp}(4,\mathbb{A}_{\mathbb{Q}})$ with trivial central character such that the archimedean component is a holomorphic discrete series representation of weight $k\ge 3$, and the non-archimedean component at $p$ is an Iwahori-spherical representation of type $\Omega$ and unramified otherwise. Using the automorphic Plancherel density theorem, we show how a limit version of our formula for $s_k(p,\Omega… CONTINUE READING

View PDF on arXiv