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

Abstract

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 {k-\frac{n}{2}+\frac{1}{2}} for Γ 0 ⁢ ( 4 ) {\Gamma_{0}(4)} , let I n ⁢ ( h ) {I_{n}(h)} be the Duke–Imamoglu–Ikeda lift of h to the space of cusp forms of weight k for Sp n ⁡ ( ℤ ) {\operatorname{Sp}_{n}({\mathbb{Z}})} . We then give an estimate of the Fourier coefficients of I n ⁢ ( h ) {I_{n}(h)} . It is better than the usual Hecke bound for the Fourier coefficients of a Siegel cusp form.