Prime geodesic theorem

DOI10.5802/jtnb.346zbMath1028.11030OpenAlexW2327307049MaRDI QIDQ1396432

Yingchun Cai

Publication date: 30 June 2003

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_2002__14_1_59_0

zbMATH Keywords

modular groupprime geodesic theorem

Mathematics Subject Classification ID

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

Related Items (15)

Gallagherian PGT on some compact Riemannian manifolds of negative curvature ⋮ Mean square in the prime geodesic theorem ⋮ Bounds on Faltings's delta function through covers ⋮ Gallagherian \(PGT\) on \(\mathrm{PSL}(2,\mathbb{Z})\) ⋮ Prime geodesics and averages of the Zagier L-series ⋮ The prime geodesic theorem in square mean ⋮ Bounds for a spectral exponential sum ⋮ The second moment for counting prime geodesics ⋮ Prime geodesic theorem for the modular surface ⋮ Sub-leading asymptotics of ECH capacities ⋮ Second moment of the Beurling zeta-function ⋮ On Kuznetsov-Bykovskii's formula of counting prime geodesics ⋮ Universality of the Selberg zeta-function forthe modular group ⋮ Prime geodesic theorem in the 3-dimensional hyperbolic space ⋮ The prime geodesic theorem for \(\mathrm{PSL}2(\mathbb{Z}[i)\) and spectral exponential sums]

Cites Work

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• Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II. Nachtrag zu Math. Ann. 142, 385-398 (1961)
• The Selberg trace formula and the Riemann zeta-function
• The Selberg trace formula for \(\mathrm{PSL}(2,\mathbb R)\). Vol. I
• On Selberg's eigenvalue conjecture
• Quantum ergodicity of eigenfunctions on \(\text{PSL}_ 2(\mathbb{Z}) \backslash H^ 2\)
• Prime geodesic theorem.
• The Character Sum Estimate with r = 3
• Class numbers of indefinite binary quadratic forms

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