2024/02/05 by Jay Jorgenson, Min Lee, Jorgenson, Jay +3 · 1 citation
Chemical Engineering · Mathematics · #Thermodynamic properties of mixtures #Functional Equations Stability Results #Advanced Mathematical Identities
paper · pdf · doi:10.48550/arxiv.2402.02959
Let M be a finite volume hyperbolic Riemann surface with arbitrary signature, and let χ be an arbitrary m-dimensional multiplier system of weight k. Let R(s,χ) be the associated Ruelle zeta function, and φ(s,χ) the determinant of the scattering matrix. We prove the functional equation that R(s,χ)φ(s,χ) = R(-s,χ)φ(s,χ)H(s,χ) where H(s,χ) is a meromorphic function of order one explicitly determined using the topological data of M and of χ, and the trigonometric function sin(s). From this, we determine the order of the divisor of R(s,χ) at s=0 and compute the lead coefficient in its Laurent expansion at s=0. When combined with results by Kitano and by Yamaguchi, we prove further instances of the Fried conjecture, which states that the R-torsion of the above data is simply expressed in terms of R(0,χ).