Small eigenvalues of the Laplace operator on compact Riemann surfaces

DOI10.1090/S0002-9904-1974-13609-8zbMath0317.30017MaRDI QIDQ4078304

Burton Randol

Publication date: 1974

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Mathematics Subject Classification ID

Spectral theory and eigenvalue problems for partial differential equations (35P99) Compact Riemann surfaces and uniformization (30F10)

Related Items (37)

On the period matrix of a Riemann surface of large genus (with an appendix by J. H. Conway and N. J. A. Sloane) ⋮ The first eigenvalue in a tower of coverings ⋮ Hecke triangle groups, transfer operators and Hausdorff dimension ⋮ Zeta functions and periodic orbit theory: A review ⋮ The Laplacian for domains in hyperbolic space and limit sets of Kleinian groups ⋮ The size of the Selberg zeta-function at places symmetric with respect to the line \(\mathrm{Re}(s)=1/2\) ⋮ Benjamini-Schramm convergence and spectra of random hyperbolic surfaces of high genus ⋮ New time-changes of unipotent flows on quotients of Lorentz groups ⋮ Poisson-Dirichlet distribution for random Belyi surfaces ⋮ GROWTH OF THE SELBERG ZETA-FUNCTION ⋮ Poincaré series for \(\mathrm{SO}(n,1)\) ⋮ Kloosterman sums and their applications: A review ⋮ Large degree covers and sharp resonances of hyperbolic surfaces ⋮ Near optimal spectral gaps for hyperbolic surfaces ⋮ Coarse non-amenability and covers with small eigenvalues. ⋮ Hyperbolic manifolds with a large number of systoles ⋮ Hardy-type results on the average of the lattice point error term over long intervals ⋮ Invariant distributions and time averages for horocycle flows ⋮ Bounds for multiplicities of automorphic representations ⋮ Poincaré series for \(SO(n,1)\) ⋮ The spectrum of Fermat curves ⋮ The role of the Ramanujan conjecture in analytic number theory ⋮ Tubes and eigenvalues for negatively curved manifolds ⋮ On Selberg's small eigenvalue conjecture and residual eigenvalues ⋮ Cubic graphs and the first eigenvalue of a Riemann surface ⋮ Geographical structure and convergence: a note on geometry in spatial growth models ⋮ Topological properties of eigenfunctions of Riemannian surfaces ⋮ The asymptotic distribution of lattice points in hyperbolic space ⋮ For every hyperbolic surface of genus \(g,\lambda_{2g-2}>1/4\) ⋮ An upper bound for λ₁ for Γ(q) and Γ₀(q) ⋮ Trivalent expanders, \((\Delta - Y)\)-transformation, and hyperbolic surfaces ⋮ ON THE MODULUS OF THE SELBERG ZETA-FUNCTIONS IN THE CRITICAL STRIP ⋮ Horocycle averages on closed manifolds and transfer operators ⋮ The \(a\)-points of the Selberg zeta-function are uniformly distributed modulo one ⋮ Density of integer points on affine homogeneous varieties ⋮ On the spectral gap for infinite index ``congruence subgroups of \(SL_2(\mathbb{Z})\) ⋮ On the spectral gap for infinite index ``congruence subgroups of SL\(_2(\mathbb{Z})\)

Cites Work

• Unnamed Item
• Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II
• On the Analytic Continuation of the Minakshisundaram-Pleijel Zeta Function for Compact Riemann Surfaces
• Correction to: Silberg' trace formua as applied to a compact riemann surface by H. P. Mckean, comm. pure appl. math. 25, pp. 225‐246,1972

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