Automorphic forms and L functions on algebraic groups

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1. Automorphic L-functions on unitary groups (joint work with A.Murase)We poved the analytic continuation and the functional equations of the standard L-function associated with a holomorphic cusp form on a unitary group. The key ingredient in the proof is a study of Shintani functions.2. Automorphic forms on unitary groups of degree 3 and primitive theta functions (joint work with A.Murase)For the study of arithmetical automorphic forms on a unitary group of degree 3, primitive theta functions are fundamental. We investigated a metaplectic representation of U(1) acting on the space of local primitive theta functions and gave its explicit irreducible decomposition.As an application, we determined the refined Fourier-Jacobi expansion of holomorphic Eisenstein series.3. theta lift and Jacobi group (joint work with A.Murase)Since Kudla lift is a restriction of Oda lift, we can construct automorphic forms on unitary groups of degree 3 from Jacobi forms explicitly. We gave another formulation of refined Fourier-Jacobi expansion of holomorphic Eisenstein series using Jacobi type Eisenstein series.