# 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, +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