Parabolic components of zeta functions

DOI10.3792/pjaa.64.21zbMath0642.10028OpenAlexW2057830819MaRDI QIDQ1101499

Nobushige Kurokawa

Publication date: 1988

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.64.21

zbMATH Keywords

asymptotic behaviourmeromorphic continuationSelberg zeta-functiondeterminant of the Laplacianspectral zeta- function

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Hurwitz and Lerch zeta functions (11M35)

Related Items (18)

The size of the Selberg zeta-function at places symmetric with respect to the line \(\mathrm{Re}(s)=1/2\) ⋮ Determinant Expression of Selberg Zeta Functions. I ⋮ Zeta functions for the Riemann zeros. ⋮ Sharpenings of Li's criterion for the Riemann hypothesis ⋮ The Selberg zeta function and the determinant of the Laplacians ⋮ Multiple sine functions and Selberg zeta functions ⋮ Selberg zeta functions and Ruelle operators for function fields ⋮ Local \(L\)-factors of motives and regularized determinants ⋮ Determinant Expression of Selberg Zeta Functions. II ⋮ Elliptic factors of Selberg zeta functions ⋮ Selberg zeta functions over function fields ⋮ Zeta Functions Over Zeros of General Zeta and L-Functions ⋮ A factorization of the Selberg zeta function attached to a rank 1 space form ⋮ On second moment of Selberg zeta-function for \(\sigma =1\) ⋮ Universality of the Selberg zeta-function forthe modular group ⋮ ON THE MODULUS OF THE SELBERG ZETA-FUNCTIONS IN THE CRITICAL STRIP ⋮ On Cramér's theorem for general Euler products with functional equation ⋮ Eigenvalues of the Laplace-Beltrami operator and the von-Mangoldt function

Cites Work

• The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
• Determinants of Laplacians
• An approach to the Selberg trace formula via the Selberg zeta-function
• Spectral functions, special functions and the Selberg zeta function
• String theories and prime number theories
• Formules de Poisson avec reste
• The asymptotic distribution of eigenvalues of the Laplace operator in an unbounded domain
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