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

par Ahlén, Olof;Gustafsson, Henrik H.P.A.;Kleinschmidt, Axel ;Liu, Baiying;Persson, Daniel
Référence Journal of number theory, 192, page (80-142)
Publication Publié, 2018-11

Article révisé par les pairs

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Résumé :

We show that Fourier coefficients of automorphic forms attached to minimal or next-to-minimal automorphic representations of SLn(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.