Determinant Expression of Selberg Zeta Functions. I

DOI10.2307/2001500zbMath0726.11036OpenAlexW4231534815MaRDI QIDQ3348044

Shin-ya Koyama

Publication date: 1991

Full work available at URL: https://doi.org/10.2307/2001500

zbMATH Keywords

determinantLaplaciananalytic continuationSelberg zeta functionspectral zeta functionlogarithmic derivative

Mathematics Subject Classification ID

Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (20)

Selberg supertrace formula for super Riemann surfaces. III: Bordered super Riemann surfaces ⋮ Selberg trace formula for bordered Riemann surfaces: Hyperbolic, elliptic and parabolic conjugacy classes, and determinants of Maass-Laplacians ⋮ Super-zeta functions and regularized determinants associated with cofinite Fuchsian groups with finite-dimensional unitary representations ⋮ On Cartier-Voros type Selberg trace formula for congruence subgroups of \(\text{PSL} (2,\mathbb{R})\) ⋮ Partial zeta functions ⋮ Functional determinant of Laplacian on Cayley projective plane \(\mathbf{P}^{2}(\text{Cay})\) ⋮ The Selberg zeta function and the determinant of the Laplacians ⋮ Explicit descriptions of spectral properties of Laplacians on spheres \(\mathbb{S}^N\) \((N\ge 1)\): a review ⋮ The distribution of zeros of the derivative of the unmodified Selberg zeta-function associated to finite volume Riemann surfaces ⋮ Selberg zeta functions and Ruelle operators for function fields ⋮ Resolvent trace formula and determinants of \(n\) Laplacians on orbifold Riemann surfaces ⋮ Determinant Expression of Selberg Zeta Functions. II ⋮ Determinants of the Laplacians on complex projective spaces \(\mathbf{P}^n(\mathbb{C})(n\geq 1)\) ⋮ Analytic torsion of complete hyperbolic manifolds of finite volume ⋮ Elliptic factors of Selberg zeta functions ⋮ A factorization of the Selberg zeta function attached to a rank 1 space form ⋮ Ruelle zeta function for cofinite hyperbolic Riemann surfaces with ramification points ⋮ Spectral asymptotics on sequences of elliptically degenerating Riemann surfaces ⋮ ON THE MODULUS OF THE SELBERG ZETA-FUNCTIONS IN THE CRITICAL STRIP ⋮ On Cramér's theorem for general Euler products with functional equation

Cites Work

• Determinants of Laplacians
• An approach to the Selberg trace formula via the Selberg zeta-function
• Spectral functions, special functions and the Selberg zeta function
• Parabolic components of zeta functions
• Determinant Expression of Selberg Zeta Functions. II
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