On the lifting of hermitian modular forms

Abstract

Let K be an imaginary quadratic field with discriminant −D. We denote by 𝒪 the ring of integers of K. Let χ be the primitive Dirichlet character corresponding to K/ℚ. Let be the hermitian modular group of degree m. We construct a lifting from S_2k(SL₂(ℤ)) to S_2k+2n(Γ_K⁽²ⁿ⁺¹⁾,det ^−k−n) and a lifting from S_2k+1(Γ₀(D),χ) to S_2k+2n(Γ_K⁽²ⁿ⁾,det ^−k−n). We give an explicit Fourier coefficient formula of the lifting. This is a generalization of the Maass lift considered by Kojima, Krieg and Sugano. We also discuss its extension to the adele group of U(m,m).