Regularized determinant formulas for the zeta functions of 3-dimensional Riemannian foliated dynamical systems
Dynamical Systems
2024-10-29 v1 Differential Geometry
Abstract
We prove a regularized determinant formula for the zeta functions of certain 3-dimensional Riemannian foliated dynamical systems, in terms of the infinitesimal operator induced by the flow acting on the reduced leafwise cohomologies. It is the formula conjectured by Deninger. The proof is based on relating the dynamical spectral -functions, analogues of the -function in analytic number theory, with the zeta function, by applying the distributional dynamical Lefschetz trace formula.
Keywords
Cite
@article{arxiv.2410.20758,
title = {Regularized determinant formulas for the zeta functions of 3-dimensional Riemannian foliated dynamical systems},
author = {Jesús A. Álvarez López and Junhyeong Kim and Masanori Morishita},
journal= {arXiv preprint arXiv:2410.20758},
year = {2024}
}