# 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} }

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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