Relating Siegel cusp forms to Siegel–Maaß forms.

In this paper we generalize a well-known isomorphism between the space of cusp forms of weight k for a Fuchsian subgroup of the first kind Γ ⊂ SL 2 (R) and the space of certain Maaß forms of weight k for Γ to an isomorphism between the space of Siegel cusp forms of weight k for a subgroup Γ ⊂ Sp n (R) , which is commensurable with the Siegel modular group Sp n (Z) , and a suitable space of Siegel–Maaß forms of weight k for Γ . [ABSTRACT FROM AUTHOR]