The Selberg zeta function for convex co-compact Schottky groups

DOI10.1007/s00220-003-1007-1zbMath1075.11059arXivmath/0211041OpenAlexW3103966093MaRDI QIDQ1422075

Kevin K. Lin, Laurent Guillopé, Maciej Zworski

Publication date: 17 February 2004

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0211041

zbMATH Keywords

holomorphic \(L^2\)-techniqueslimit-set quasi-self-similarityRuelle transfer-operator determinants

Mathematics Subject Classification ID

Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Determinants and determinant bundles, analytic torsion (58J52)

Related Items (41)

Explicit spectral gaps for random covers of Riemann surfaces ⋮ Resonances for open quantum maps and a fractal uncertainty principle ⋮ Hecke triangle groups, transfer operators and Hausdorff dimension ⋮ Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions ⋮ A note on the resonance counting function for surfaces with cusps ⋮ Resonances and density bounds for convex co-compact congruence subgroups of \(\mathrm{SL}_2(\mathbb Z)\) ⋮ Fractal Weyl laws for asymptotically hyperbolic manifolds ⋮ Density of resonances for covers of Schottky surfaces ⋮ Scattering phase asymptotics with fractal remainders ⋮ Fractal upper bounds on the density of semiclassical resonances ⋮ Distribution of resonances for open quantum maps ⋮ Ulam method and fractal Weyl law for Perron-Frobenius operators ⋮ Global normal form and asymptotic spectral gap for open partially expanding maps ⋮ Uniform hyperbolicity of a class of scattering maps ⋮ Weyl laws for open quantum maps ⋮ Generalization of Selberg's \(\frac {3}{16} \) theorem and affine sieve ⋮ Resonances for graph directed Markov systems ⋮ Explicit eigenvalue estimates for transfer operators acting on spaces of holomorphic functions ⋮ Fractal Weyl laws and wave decay for general trapping ⋮ Exponential mixing of geodesic flows for geometrically finite hyperbolic manifolds with cusps ⋮ Group actions and harmonic analysis in number theory. Abstracts from the workshop held May 7--12, 2023 ⋮ Fractal Weyl law for open quantum chaotic maps ⋮ On the critical line of convex co-compact hyperbolic surfaces ⋮ Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps ⋮ Upper bound on the density of Ruelle resonances for Anosov flows ⋮ Density and location of resonances for convex co-compact hyperbolic surfaces ⋮ On the Ruelle eigenvalue sequence ⋮ Explicit a priori bounds on transfer operator eigenvalues ⋮ Resonances for asymptotically hyperbolic manifolds: Vasy's method revisited ⋮ Expanding maps on Cantor sets and analytic continuation of zeta functions ⋮ Mathematical study of scattering resonances ⋮ Distribution of Resonances for Hyperbolic Surfaces ⋮ Uniform exponential mixing and resonance free regions for convex cocompact congruence subgroups of $\operatorname {SL}_2(\mathbb {Z})$ ⋮ A thermodynamic formalism approach to the Selberg zeta function for Hecke triangle surfaces of infinite area ⋮ Wave decay on convex co-compact hyperbolic manifolds ⋮ Numerical resonances for Schottky surfaces via Lagrange–Chebyshev approximation ⋮ Meromorphic continuation of Selberg zeta functions with twists having non-expanding cusp monodromy ⋮ A transfer-operator-based relation between Laplace eigenfunctions and zeros of Selberg zeta functions ⋮ Zeros of the Selberg zeta function for symmetric infinite area hyperbolic surfaces ⋮ Resonance projectors and asymptotics for 𝑟-normally hyperbolic trapped sets ⋮ Resonance chains and geometric limits on Schottky surfaces

Uses Software

• ARPACK

Cites Work

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