# 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} }

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

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