ON THE CONVERGENCE OF ZETA FUNCTIONS OF PREHOMOGENEOUS VECTOR SPACES

被引：0

作者：

Finis, Tobias ^{[1
]}

Lapid, Erez ^{[2
]}

机构：

[1] Univ Leipzig, Inst Math, Leipzig, Germany

[2] Weizmann Inst Sci, Dept Math, Rehovot, Israel

来源：

NAGOYA MATHEMATICAL JOURNAL | 2025年

关键词：

zeta functions; prehomogeneous vector spaces; nilpotent orbits; MEAN-VALUE THEOREM; DIRICHLET SERIES; CLASS-NUMBERS; COEFFICIENTS; SUBGROUPS;

D O I：

10.1017/nmj.2024.34

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a general convergence result for zeta functions of prehomogeneous vector spaces extending results of H. Saito, F. Sato and Yukie. Our analysis points to certain subspaces which yield boundary terms. We study it further in the setup arising from nilpotent orbits. In certain cases we determine the residue at the rightmost pole of the zeta function.

引用

页数：46

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