Study on automorphic forms, automorphic L functions and Shintani functions.

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1. Shintani functions (joint work with A. Murase and S. Kato)We proved the multiplicity one property and explicit formulae of Whittaker-Shintani functions for split orthogonal groups.2. Automorphic forms on unitary groups of degree 3 (joint work with A. Murase)(1) We determined the refined Fourier-Jacobi expansion of holomorphic Eisenstein series and proved the algebraicity of Fourier-Jacobi coefficients.(2) We determined the refinedd Fourier-Jacobi expansion of Kudla lift. We gave another proof of the Hecke compatibility of Kudla lift.3. Construction of automorphic forms(1) We constructed many automorphic forms on unitary groups of degree 3 explicity using Jacobi forms. Since their Taylor expansion can be writtten explictly, these forms will be used to determine the structure of the graded algebra.(2) We started the study of Fourier expansion of Eisenstein series on 0(n+1,1) induced from automorphic forms on O(n). We hope that non-constant terms are described by using Shintani functions.