On Fourier coefficients of automorphic forms of symplectic groups
For a number of reasons it is interesting to determine Fourier coefficients of automorphic forms. The best known Fourier coefficient is the so-called Whittaker Fourier coefficient. While every cuspidal representation of \(\text{GL}_n(\mathbb A)\) has such a Fourier coefficient, for other classical groups this is not true. In the paper under the review, the authors study Fourier coefficients of cuspidal representations on symplectic groups. They associate to each unipotent orbit a set of Fourier coefficients of an automorphic form on \(\text{Sp}_{2n}\) or its double cover. They prove that every cuspidal representation on a symplectic group has a non-trivial Fourier coefficient with respect to a certain type of unipotent class.
scientific article; zbMATH DE number 1945292