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Fourier coefficients attached to small automorphic representations of SLn (A)

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Ahlen,  Olof
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Kleinschmidt,  Axel
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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1707.08937.pdf
(Preprint), 760KB

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Citation

Ahlen, O., Gustafsson, H. P. A., Kleinschmidt, A., Liu, B., & Persson, D. (2018). Fourier coefficients attached to small automorphic representations of SLn (A). Journal of Number Theory, 192, 80-142. doi:10.1016/j.jnt.2018.03.022.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002D-DB41-2
Abstract
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 scattering amplitudes in string theory.