Fourier coefficients attached to small automorphic representations of SLn(A)
Fourier coefficients attached to small automorphic representations of SLn(A)
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DOI：
10.1016/j.jnt.2018.03.022
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发表时间：
2018-11
影响因子：
0.7
通讯作者：
O. Ahlén;H. Gustafsson;A. Kleinschmidt;Baiying Liu;D. Persson
中科院分区：
文献类型：
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作者：
O. Ahlén;H. Gustafsson;A. Kleinschmidt;Baiying Liu;D. Persson
我们证明了SL n（A）的极小或次极小自守表示的自守形式的傅立叶系数完全由某些高度退化的Whittaker系数决定。我们给出了一个明确的公式的傅立叶展开，类似于Piatetski-Shapiro-Shalika公式。此外，我们推导出与所有极大抛物子群相关的傅立叶系数的表达式。这些结果对于弦理论中的散射振幅有潜在的应用。
We show that Fourier coefficients of automorphic forms attached to minimal or next-to-minimal automorphic representations of SL n (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.