A mean value theorem for closed geodesics on congruence surfaces

DOI10.1515/FORUM.2007.034zbMath1127.53033arXivmath/0502254MaRDI QIDQ5426548

Vladimir Lukianov

Publication date: 13 November 2007

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0502254

zbMATH Keywords

hyperbolic LaplacianRiemann surfaceclosed geodesicseigenvalue statisticscongruence surfacesmean square of weighted multiplicitiesweighted multiplicity function

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Geodesics in global differential geometry (53C22) Fourier coefficients of automorphic forms (11F30) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (1)

Square integrals of the logarithmic derivatives of Selberg’s zeta functions in the critical strip

Cites Work

• Unnamed Item
• Distribution of eigenvalues for the modular group
• Class numbers of indefinite binary quadratic forms
• The limit distribution of a number theoretic function arising from a problem in statistical mechanics
• The correlation between multiplicities of closed geodesics on the modular surface

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