Gallagherian PGT on some compact Riemannian manifolds of negative curvature

DOI10.1007/s40840-022-01273-5zbMath1490.11088OpenAlexW4226209882WikidataQ115371686 ScholiaQ115371686MaRDI QIDQ2147606

Dženan Gušić

Publication date: 20 June 2022

Published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40840-022-01273-5

zbMATH Keywords

Riemannian manifoldsprime geodesic theoremcounting functionsSelberg and Ruelle zeta functions

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Refinement of prime geodesic theorem
• Class numbers of orders in cubic fields
• Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II
• Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II. Nachtrag zu Math. Ann. 142, 385-398 (1961)
• The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
• Zeta function of Selberg's type for compact quotient of SU(n,1) (n\(\geq 2)\)
• Analytic torsion and Ruelle zeta functions for hyperbolic manifolds with cusps
• The zeta functions of Ruelle and Selberg for hyperbolic manifolds with cusps
• Zeta functions of Selberg's type associated with homogeneous vector bundles
• Analytic torsion and closed geodesics on hyperbolic manifolds
• Torsion and closed geodesics on complex hyperbolic manifolds
• Spectra of compact locally symmetric manifolds of negative curvature
• Selberg type zeta functions for the group of complex two by two matrices of determinant one
• Zeta-functions for expanding maps and Anosov flows
• The Selberg trace formula for \(\mathrm{PSL}(2,\mathbb R)\). Vol. I
• Zeta functions of Selberg's type for compact space forms of symmetric spaces of rank one
• The length spectra of some compact manifolds of negative curvature
• The Selberg trace formula and the Selberg zeta-function for cocompact discrete subgroups of \(SO_ +(1,n)\)
• Spectral estimates for compact hyperbolic space forms and the Selberg zeta function for \(p\)-spectra. II
• Prime geodesic theorem
• On Koyama's refinement of the prime geodesic theorem
• Gallagherian \(PGT\) on \(\mathrm{PSL}(2,\mathbb{Z})\)
• \(R\)-torsion and zeta functions for locally symmetric manifolds
• Higher torsion zeta functions
• On Selberg's eigenvalue conjecture
• Quantum ergodicity of eigenfunctions on \(\text{PSL}_ 2(\mathbb{Z}) \backslash H^ 2\)
• Order of Selberg's and Ruelle's zeta functions for compact even-dimensional locally symmetric spaces
• Gallagherian prime geodesic theorem in higher dimensions
• Prime geodesic theorem for the Picard manifold
• A prime geodesic theorem of Gallagher type for Riemann surfaces
• A prime geodesic theorem for \(\mathrm{SL}_4\)
• ON THE ERROR TERM IN THE PRIME GEODESIC THEOREM
• Prime geodesic theorem.
• The zeta functions of Ruelle and Selberg. I
• Some consequences of the Riemann hypothesis
• On the prime geodesic theorem for hyperbolic 3‐manifolds
• The prime geodesic theorem
• On the logarithmic derivative of zeta functions for compact even-dimensional locally symmetric spaces of real rank one
• Errata and addendum to “On the prime geodesic theorem for hyperbolic ‐manifolds” Math. Nachr. 291 (2018), no. 14–15, 2160–2167