Selberg trace formula for bordered Riemann surfaces: Hyperbolic, elliptic and parabolic conjugacy classes, and determinants of Maass-Laplacians

DOI10.1007/BF02102007zbMath0837.11033MaRDI QIDQ1330955

Christian Grosche, Jens Bolte

Publication date: 10 August 1994

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

zbMATH Keywords

automorphic formsSelberg trace formulabordered Riemann surfacesdeterminants of Maass-LaplaciansDirichlet and Neumann boundary-conditionsFuchsian groups of the first kindhyperbolic, elliptic and parabolic conjugacy classesopen bosonic string theory

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) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Riemann surfaces (30F99)

Related Items (4)

Kloosterman sums and their applications: A review ⋮ Explicit descriptions of spectral properties of Laplacians on spheres \(\mathbb{S}^N\) \((N\ge 1)\): a review ⋮ Numerical computations with the trace formula and the Selberg eigenvalue conjecture ⋮ On the relative distribution of eigenvalues of exceptional Hecke operators and automorphic Laplacians

Cites Work

• A superanalog of the Selberg trace formula and multiloop contributions for fermionic strings
• The Polyakov path integral over bordered surfaces (the open string amplitudes)
• On cusp forms for co-finite subgroups of PSL(2,\({\mathbb{R}})\)
• Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen
• Determinants of Dirac operators and Thirring model partition functions on Riemann surfaces with boundaries
• Determinants of Laplace-like operators on Riemann surfaces
• Classical and quantum mechanics of a strongly chaotic billiard system
• The quantization of a classically ergodic system
• On determinants of Laplacians on Riemann surfaces
• Theta functions, modular invariance, and strings
• On the distribution of the lengths of closed geodesics of a compact surface with totally geodesic boundary.
• Determinants of Laplacians
• Heat kernels and super-determinants of Laplace operators on super-Riemann surfaces
• Determinants of Laplacians on surfaces of finite volume
• Feynman path integrals and the trace formula for the Schrödinger operators
• Selberg super-trace formula for super Riemann surfaces. II: Elliptic and parabolic conjugacy classes, and Selberg super-zeta functions
• The Selberg trace formula for \(\mathrm{PSL}(2,\mathbb R)\). Vol. I
• The Selberg trace formula for bordered Riemann surfaces
• Selberg supertrace formula for super Riemann surfaces. III: Bordered super Riemann surfaces
• Determinant Expression of Selberg Zeta Functions. I
• SPECTRAL THEORY OF AUTOMORPHIC FUNCTIONS, THE SELBERG ZETA-FUNCTION, AND SOME PROBLEMS OF ANALYTIC NUMBER THEORY AND MATHEMATICAL PHYSICS
• BORDERED RIEMANN SURFACES, SCHOTTKY GROUPS AND OFF-SHELL STRING AMPLITUDES
• Novel rule for quantizing chaos
• Symmetric Fuchsian Groups
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