Automorphic forms and L functions on algebraic groups

1.酉群上的自守L-函数（与A.Murase共同工作）给出了酉群上与全纯尖形相联系的标准L-函数的解析延拓和函数方程。证明的关键要素是对Shintani函数的研究。2.自守形式的酉群的程度3和原始theta函数（联合工作与A.村濑）为研究算术自守形式的酉群的程度3，原始theta函数是基本的。研究了U（1）在局部本原theta函数空间上的亚代数表示，给出了它的显式不可约分解，作为应用，确定了全纯Eisenstein级数的精化Fourier-Jacobi展开式.θ提升和Jacobi群（与A.Murase共同工作）由于Kudla提升是Oda提升的限制，我们可以从Jacobi形式明确地构造3次酉群上的自守形式。利用Jacobi型Eisenstein级数给出了全纯Eisenstein级数的另一种精化Fourier-Jacobi展开式。

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.