Estimates for the Fourier coefficients of the Duke-Imamoglu-Ikeda lift

TL;DR

This paper provides improved estimates for the Fourier coefficients of the Duke-Imamoglu-Ikeda lift, a specific type of Siegel cusp form, surpassing traditional bounds and enhancing understanding of their growth behavior.

Contribution

The authors derive sharper bounds for Fourier coefficients of the Duke-Imamoglu-Ikeda lift, advancing the analytic understanding of these automorphic forms.

Findings

Fourier coefficient estimates are improved over classical Hecke bounds.

The results apply to lifts from Kohnen plus subspace forms.

Enhanced bounds facilitate better analysis of automorphic forms.

Abstract

Let $k$ and $n$ be positive even integers. For a Hecke eigenform $h$ in the Kohnen plus subspace of weight $k-n/2+1/2$ for $\varGamma_0(4)$, let $I_n(h)$ be the Duke-Imamoglu-Ikeda lift of $h$ to the space of cusp forms of weight $k$ for $Sp_n(\mathbb Z)$. We then give an estimate of the Fourier coefficients of $I_n(h)$. It is better than the usual Hecke bound for the Fourier coefficients of a Siegel cusp form.