Studies on arithmetic automorphic forms and zeta functions

(6)酉群的亚辛表示的一种新的分裂和Howe特征标公式的一个简单证明。在这个研究项目中，我们研究了酉群上的自同构形，特别是它们的算术性，以及局部域上代数群的相关表示理论。我们的主要结果总结如下：(1)U(1)上的epsilon二分法的一个新的简单证明和改进；(2)U(2，1)上自同构形的傅立叶-雅可比展开式理论的改写和补充；(3)U(2，1)上全纯Eisenstein级数的傅立叶-雅可比展开式的显式计算；(4)U(2，1)上全纯Eisenstein级数的傅立叶-雅可比展开式的非零化判据

(6) A New splitting of metaplectic representations of unitary groups and a simple proof of Howe's character formulaIn this research project, we studies automorphic forms on unitary groups, in particular their arithmeticity, and related representation theory of algebraic groups over local fields. Our main results, which are joint works with T.Sugano except 6, are summarized as follows.(1) A New simple proof and refinement of epsilon dichotomy for U(1)(2) Adelic reformulation and refiment of the theory of Fourier-Jacobi expansion of automorphic forms on U(2,1) originally due to T.Shintani(3) Explicit calculation of Fourier-Jacobi expansion of holomorphic Eisenstein series on U(2,1)(4) A criterion for the non-vanishing of Fourier-Jacobi expansion of holomorphic Eisenstein series on U(2,1) in terms of the critical central values of Hecke L-functions(5) Adelic reformulation of Kudla lift