A Maass space in higher genus

Abstract

We show that for arbitrary even genus 2 n with $n\equiv {0,1}$ (mod 4) the subspace of Siegel cusp forms of weight $k+n$ generated by the Ikeda lifts of elliptic cusp forms of weight 2 k can be characterized by certain simple relations among the Fourier coefficients. These generalize the classical Maass relations in genus 2.