一类2类幂零李环的理想ζ函数

IF 0.6 4区数学 Q3 MATHEMATICS

Quarterly Journal of Mathematics Pub Date : 2020-03-01 DOI:10.1093/qmathj/haaa010

Christopher Voll

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引用次数: 5

摘要

在M. N. Berman, B. Klopsch和U. Onn (A族2类幂零群，它们的自同构和亲同构zeta函数，数学)中，我们给出了与无限族-2类幂零李环的成员相关的各种理想zeta函数的显式公式。Z. 290(2018)， 909935)，根据Igusa函数。作为推论，我们得到了关于全局理想zeta函数、局部泛函方程、拓扑、约化和分级理想zeta函数的解析性质，以及与李环相关的单幂群格式的表示zeta函数。

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IDEAL ZETA FUNCTIONS ASSOCIATED TO A FAMILY OF CLASS-2-NILPOTENT LIE RINGS

We produce explicit formulae for various ideal zeta functions associated to the members of an infinite family of class- $2$ -nilpotent Lie rings, introduced in M. N. Berman, B. Klopsch and U. Onn (A family of class-2 nilpotent groups, their automorphisms and pro-isomorphic zeta functions, Math. Z. 290 (2018), 909935), in terms of Igusa functions. As corollaries we obtain information about analytic properties of global ideal zeta functions, local functional equations, topological, reduced and graded ideal zeta functions, as well as representation zeta functions for the unipotent group schemes associated to the Lie rings in question.

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来源期刊

Quarterly Journal of Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. All major areas of pure mathematics are represented on the editorial board.