On the lifting of hermitian modular forms

Abstract

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 $\Gamma ^{(m)}_K=\mathrm {U} (m,m)({\mathbb Q})\cap \mathrm {GL}_{2m}({\cal O})$ be the hermitian modular group of degree m . We construct a lifting from S 2 k ( SL 2 (ℤ)) to S 2 k +2 n (Γ K (2 n +1) ,det − k − n ) and a lifting from S 2 k +1 (Γ 0 ( D ), χ ) to S 2 k +2 n (Γ K (2 n ) ,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 ).

Locations

• Compositio Mathematica - View - PDF