Functional equations of prehomogeneous zeta functions and intertwining operators

Fumihiro Sato

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Functional equations of prehomogeneous zeta functions and intertwining operators

机译：齐次zeta函数的函数方程和交织算子

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摘要

We establish a relation between the gamma matrices of the functional equations satisfied by zeta functions associated with prehomogeneous vector spaces and certain integrals related to the intertwining operator of degenerate principal series representations of general linear groups.

机译：我们建立由zeta函数满足的函数方程的γ矩阵与前同矢量空间相关的关系，以及与一般线性群的简并主序列表示的交织算子有关的某些积分之间的关系。

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来源
《Journal of the Mathematical Society of Japan》 |2006年第4期|p.995-1008|共14页
作者
Fumihiro Sato;
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作者单位

Department of Mathematics Rikkyo University Nishi-Ikebukuro, Toshima-ku Tokyo 171-8501, Japan;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类数学;
关键词
zeta function; prehomogeneous vector space; degenerate principal series; intertwining operator;

机译：zeta函数;齐次向量空间;退化主级;交织算子;

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专利

1. Zeta functions in several variables associated with prehomogeneous vector spaces, I. Functional equations [J] . Fumihiro Sato Proceedings of the Japan Academy, Series A. Mathematical Sciences . 1981,第1期

机译：Zeta函数在与前同向量空间相关的几个变量中，I。函数方程
2. The functional equation of zeta distributions associated with prehomogeneous vector spaces $(~G,~ho,M(n,{f C}))$ [J] . Yasuo Teranishi Nagoya Mathematical Journal . 1985,第2期

机译：与前同矢量空间$（〜G，〜 rho，M（n，{ bf C}））$相关的zeta分布的函数方程
3. On Residues of Intertwining Operators in Cases with Prehomogeneous Nilradical [J] . Varma Sandeep Canadian Journal of Mathematics . 2017,第5期

机译：在逆胆管不可岩中的杂交运营商残留
4. On the Functional Equation for the Hurwitz Zeta-function [C] . Yang Ming-shun International Conference on Artificial Intelligence and Computational Intelligence;AICI '09 . 2009

机译：关于Hurwitz Zeta函数的函数方程
5. A functional equation for a prehomogeneous vector space and unitary representations of GL(2n, R) [D] . Lee, Juhyung 2012

机译：齐次向量空间的函数方程和GL（2n，R）的unit表示
6. On Zeta Functions Associated with Prehomogeneous Vector Spaces [O] . Mikio Sato, Takuro Shintani 1972

机译：与齐次向量空间相关的Zeta函数
7. ON FUNCTIONAL EQUATIONS OF PREHOMOGENEOUS ZETA DISTRIBUTIONS OVER A LOCAL FIELD OF CHARACTERISTIC P(Theory of prehomogeneous vector spaces) [O] . KIMURA TATSUO, FUJINAGA MAKIKO, KOGISO TAKEYOSHI 1995

机译：特征P的局部场上前均相Zeta分布的函数方程（前均相空间理论）
8. Functional Equation for Dynamical Zeta Functions of Milnor-Thurston Type [R] . Ruelle, D. 1994

机译：milnor-Thurston型动力Zeta函数的泛函方程

Functional equations of prehomogeneous zeta functions and intertwining operators

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