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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与2级-耐力李环族相关的理想ZETA函数

我们为与无穷大类- | $ 2 $ |的成员相关的各种理想zeta函数产生显式公式。-nilpotent Lie环，在MN Berman，B.Klopsch和U.Onn（二类Nilpotent组的族，它们的自同构和同构同位zeta函数，Math。Z . 290（2018），909935）中引入的功能。作为推论，我们获得有关全局理想zeta函数，局部函数方程，拓扑，归约和渐变的理想zeta函数的解析性质的信息，以及与相关Lie环相关的单能组方案的表示zeta函数。