Asymptotics and zeta functions on compact nilmanifolds

Veronique Fischer

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arXiv · 2112.01246

Asymptotics and zeta functions on compact nilmanifolds

Veronique Fischer

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Abstract

In this paper, we obtain asymptotic formulae on nilmanifolds $\Gamma \backslash G$, wher $G$ is any stratified (or even graded) nilpotent Lie group equipped with a co-compact discrete subgroup $\Gamma$. We study especially the asymptotics related to the sub-Laplacians naturally coming from the stratified structure of the group $G$ (and more generally any positive Rockland operators when $G$ is graded). We show that the short-time asymptotic on the diagonal of the kernels of spectral multipliers contains only a single non-trivial term. We also study the associated zeta functions.

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BibTeX RIS

Veronique Fischer. 2021-11-18. Asymptotics and zeta functions on compact nilmanifolds. https://arxiv.org/abs/2112.01246

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