On fundamental Fourier coefficients of Siegel modular forms

Siegfried Bocherer, Soumya Das

Published 2018-10-01Version 1

We prove that if $F$ is a non-zero (possibly non-cuspidal) vector-valued Siegel modular form of any degree, then it has infinitely many non-zero Fourier coefficients which are indexed by half-integral matrices having odd, square-free (and thus fundamental) discriminant. The proof uses an induction argument in the setting of vector-valued modular forms.