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

JOURNAL OF NUMBER THEORY

卷:192

Article

Ahlen, Olof¹  Gustafsson, Henrik P. A.^2,3  Kleinschmidt, Axel^1,4  Liu, Baiying⁵  Persson, Daniel⁶ 

[1] Max Planck Inst Gravitat Phys, Albert Einstein Inst, Muhlenberg 1, D-14476 Potsdam, Germany

[2] Chalmers Univ Technol, Dept Phys, SE-41296 Gothenburg, Sweden

[3] Stanford Univ, Dept Math, Stanford, CA 94305 USA

[4] ULB, Solvay Inst, Campus Plaine CP231, BE-1050 Brussels, Belgium

[5] Purdue Univ, Dept Math, 150 N Univ St, W Lafayette, IN 47907 USA

[6] Chalmers Univ Technol, Dept Math Sci, SE-41296 Gothenburg, Sweden

关键词: Small automorphic forms;    Fourier coefficients;    Fourier expansion;    Nilpotent orbits;    String Theory;    Scattering amplitudes;   

DOI  :  10.1016/j.jnt.2018.03.022

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free