Corpus ID: 119625589

# Fourier coefficients attached to small automorphic representations of ${\mathrm{SL}}_n(\mathbb{A})$

@article{Ahlen2017FourierCA,
title={Fourier coefficients attached to small automorphic representations of \$\{\mathrm\{SL\}\}_n(\mathbb\{A\})\$},
author={O. Ahl'en and H. Gustafsson and A. Kleinschmidt and B. Liu and D. Persson},
journal={arXiv: Representation Theory},
year={2017}
}
• O. Ahl'en, +2 authors D. Persson
• Published 2017
• Mathematics, Physics
• arXiv: Representation Theory
• We show that Fourier coefficients of automorphic forms attached to minimal or next-to-minimal automorphic representations of ${\mathrm{SL}}_n(\mathbb{A})$ are completely determined by certain highly degenerate Whittaker coefficients. We give an explicit formula for the Fourier expansion, analogously to the Piatetski-Shapiro-Shalika formula. In addition, we derive expressions for Fourier coefficients associated to all maximal parabolic subgroups. These results have potential applications for… CONTINUE READING