On Arakawa lifting

By modular forms one would usually have holomorphic one in mind. Arakawa lifting is a theta lifting construction of non-holomorphic but real analytic automorphic forms on the indefinite symplectic group Sp(1,1) or real hyperbolic space of dimension four. The notion of the theta lifting is a generalization of theta functions, whose representation theoretic formulation is known as theta correspondence or Howe 
correspondence. The aim of this talk is to report a recent progress on arithmetic results on Arakawa lifts such as their automorphic L-functions in relation with their norms called the Petersson norm.