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

作者：Ahlen Olof; Gustafsson Henrik P A; Kleinschmidt Axel^*; Liu Baiying; Persson Daniel

来源：Journal of Number Theory, 2018, 192: 80-142.

DOI：10.1016/j.jnt.2018.03.022

• Small automorphic forms
• Fourier coefficients
• Fourier expansion
• Nilpotent orbits
• String Theory
• Scattering amplitudes

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.

• 出版日期2018-11