A Maass space in higher genus

Abstract

We show that for arbitrary even genus 2n with n ≡ 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 2k can be characterized by certain simple relations among the Fourier coefficients. These generalize the classical Maass relations in genus 2. © Foundation Compositio Mathematica 2005.