Pro-isomorphic zeta functions of some $D^\ast$ Lie lattices of even rank

Yifat Moadim-Lesimcha; Michael M. Schein

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arXiv · 2205.00419

Pro-isomorphic zeta functions of some $D^\ast$ Lie lattices of even rank

Yifat Moadim-Lesimcha·Michael M. Schein

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Abstract

We compute the local pro-isomorphic zeta functions at all but finitely many primes for a certain family of class-two-nilpotent Lie lattices of even rank, parametrized by irreducible non-linear polynomials $f(x) \in \mathbb{Z} [x]$, that corresponds to a family of groups introduced by Grunewald and Segal. The result is expressed in terms of a combinatorially defined family of rational functions satisfying a functional equation upon inversion of the variables.

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BibTeX RIS

Yifat Moadim-Lesimcha, Michael M. Schein. 2022-05-01. Pro-isomorphic zeta functions of some $D^\ast$ Lie lattices of even rank. https://arxiv.org/abs/2205.00419

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