An analytic zeta function ramp at the black hole Thouless time
Abstract
A bstract Black hole normal modes have intriguing connections to logarithmic spectra, and the spectral form factor (SFF) of E n = log n is the mod square of the Riemann zeta function ζ ( s ). In this paper, we first provide an analytic understanding of the dip-ramp-plateau structure of ζ ( s ) and show that the ramp at $$ \beta \equiv \mathfrak{R}(s)=0 $$ β ≡ R s = 0 has a slope precisely equal to 1. The s = 1 pole of ζ ( s ) can be viewed as due to a Hagedorn transition in this setting, and Riemann’s analytic continuation to $$ \mathfrak{R}(s)
Fields of Study & Subjects
Black Holes and Theoretical Physics
Algebraic Geometry and Number Theory
Advanced Mathematical Identities
Publication details
- Journal / source
- Journal of High Energy Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 2026
- Issue
- 2
- Publication date
- 2 February 2026
- Language
- EN