An explicit formula of the unramified Shintani functions for $(\mathbf{GSp}_{4},\mathbf{GL}_{2} \times_{\mathbf{GL}_{1}} \mathbf{GL}_{2})$ and its application

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Kohta Gejima¹ 

[1] Department of Mathematics, Graduate School of Science, Osaka University

关键词: Finite difference method;    nonlinear partial differential equations;    Cauchy problem;    ill-posed problems.;   

DOI  :  10.3792/pjaa.93.105

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

Let $F$ be a non-archimedean local field of arbitrary characteristic. In this paper, we announce an explicit formula of the unramified Shintani functions for $(\mathbf{GSp}_{4}(F),(\mathbf{GL}_{2} \times_{\mathbf{GL}_{1}} \mathbf{GL}_{2})(F))$. As an application, we compute a local zeta integral, which represents the spin $L$-factor of $\mathbf{GSp}_{4}$.

【 授权许可】

Unknown