Fourier coefficients of minimal and next-to-minimal automorphic representations of simply-laced groups

@article{Gourevitch2019FourierCO,
  title={Fourier coefficients of minimal and next-to-minimal automorphic representations of simply-laced groups},
  author={D. Gourevitch and H. Gustafsson and A. Kleinschmidt and D. Persson and S. Sahi},
  journal={arXiv: Number Theory},
  year={2019}
}
  • D. Gourevitch, H. Gustafsson, +2 authors S. Sahi
  • Published 2019
  • Mathematics, Physics
  • arXiv: Number Theory
  • In this paper we analyze Fourier coefficients of automorphic forms on adelic split simply-laced reductive groups $G(\mathbb{A})$. Let $\pi$ be a minimal or next-to-minimal automorphic representation of $G(\mathbb{A})$. We prove that any $\eta\in \pi$ is completely determined by its Whittaker coefficients with respect to (possibly degenerate) characters of the unipotent radical of a fixed Borel subgroup, analogously to the Piatetski-Shapiro--Shalika formula for cusp forms on $GL_n$. We also… CONTINUE READING

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    Eisenstein series and automorphic representations
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