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

1. Shintani函数（与A.村濑和S. Kato）证明了可裂正交群的Whittaker-Shintani函数的重数为1的性质和显式公式. 3度酉群上的自守形式（与A.（1）确定了全纯Eisenstein级数的精化Fourier-Jacobi展开式，并证明了Fourier-Jacobi系数的代数性。(2)我们确定了Kudla升力的改进的Fourier-Jacobi展开式。我们给出了Kudla升力的Hecke相容性的另一个证明。自守形式的构造（1）利用Jacobi形式在3次显酉群上构造了许多自守形式。由于它们的泰勒展开式可以显式表示，因此这些形式将被用来确定分次代数的结构。(2)我们从O（n+1，1）上的自守形式出发，研究了Eisenstein级数在O（n+1，1）上的Fourier展开.我们希望用Shintani函数来描述非常数项。

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.