Estimates for the Fourier coefficients of the Duke-Imamoglu-Ikeda lift (Q6133253)

The aim of the paper under review is to give a better estimate for the Fourier coefficients of the Duke-Imamoglu-Ikeda lift. Let \(k\) and \(n\) positive even integers. Consider the Duke-Imamoglu-Ikeda lift \(I_n(h)\) of a cuspidal Hecke eigenform \(h\) in \(S_{k-n/2+1/2}^+(\Gamma_0(4))\) to \(S_k(\Gamma^{(n)})\) where \(\Gamma^{(n)}\) denotes the Siegel modular group of genus \(n\). In the paper under review, the authors give an estimate of the Fourier coefficients of \(I_n(h)\) which is a better estimate than the usual Hecke bound for the Fourier coefficients of a Siegel cusp form.