On Fourier Coefficients of Automorphic Forms of GL(n)

Dihua Jiang, Baiying Liu
2012 International mathematics research notices  
It is a well-known theorem, due to J. Shalika and I. Piatetski-Shapiro, independently, that any non-zero cuspidal automorphic form on GL n (A) is generic, i.e. has a non-zero Whittaker-Fourier coefficient. Its proof follows from the Fourier expansion of the cuspidal automorphic form in terms of its Whittaker-Fourier coefficients. In this paper, we extend this Fourier expansion to the whole discrete spectrum of the space of all square-integrable automorphic forms of GL n (A) and determine the
more » ... rier coefficients of irreducible non-cuspidal (residual) automorphic representations of GL n (A) in terms of unipotent orbits.
doi:10.1093/imrn/rns153 fatcat:gpmjcpqhsvdf7d3twsmajt5az4