Maass relations in higher genus

TL;DR

This paper characterizes the subspace of Siegel cusp forms of even genus generated by Ikeda lifts through specific Fourier coefficient relations, extending previous work by Kohnen and Kojima.

Contribution

It generalizes the Maass relations to higher genus Siegel cusp forms, providing a new characterization of Ikeda lift-generated subspaces.

Findings

Identifies linear relations among Fourier coefficients for higher genus forms.

Extends Maass relations to genus 2n.

Provides a new framework for understanding Ikeda lifts.

Abstract

For an arbitrary even genus $2n$ we show that the subspace of Siegel cusp forms of degree $2n$ generated by Ikeda lifts of elliptic cusp forms can be characterized by certain linear relations among Fourier coefficients. This generatizes the work of Kohnen and Kojima.