Linear dependence among Siegel modular forms (Q1591378)

The authors give new criteria that describe when high enough vanishing at the cusps implies that a Siegel cusp form is zero. Classically Siegel gave such criteria relating the trace function. Namely, he showed that a Siegel cusp form is zero if the Fourier coefficients \(a_s\) vanish for all \(s\) such that \(\text{tr}(s)\leq c(k,n)\) where \(c(k,n)\) is a constant depending only on \(k\) (the weight) and \(n\) (the degree). However his result is impractical for \(n> 1\). The authors introduce a certain class function (the dyadic trace function) and improve Siegel's criterion. In the final part, they give numerical examples which show the advantage of their criteria.