Regularized determinant formulas for the zeta functions of 3-dimensional Riemannian foliated dynamical systems

2024/10/28 by Jesús A. Álvarez López, López, Jesús A. Álvarez, Kim Junhyeong +3
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Quantum chaos and dynamical systems #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2410.20758

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 ξ-functions, analogues of the ξ-function in analytic number theory, with the zeta function, by applying the distributional dynamical Lefschetz trace formula.

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