The prime geodesic theorem in square mean

DOI10.1016/j.jnt.2018.10.012zbMath1461.11082arXiv1805.07461OpenAlexW2963312805MaRDI QIDQ1710763

András Biró, Gergely Harcos, Antal Balog, Péter Maga

Publication date: 23 January 2019

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.07461

zbMATH Keywords

prime geodesic theoremspectral exponential sums

Mathematics Subject Classification ID

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)

Related Items (7)

Prime geodesics and averages of the Zagier L-series ⋮ Gallagherian prime geodesic theorem in higher dimensions ⋮ The second moment for counting prime geodesics ⋮ On von Koch theorem for \(\mathrm{PSL}(2,\mathbb{Z})\) ⋮ Second moment of the prime geodesic theorem for \(\mathrm{PSL}(2, \mathbb{Z}[i)\)] ⋮ Effective bounds for Huber’s constant and Faltings’s delta function ⋮ The prime geodesic theorem for \(\mathrm{PSL}2(\mathbb{Z}[i)\) and spectral exponential sums]

Cites Work

• Local average in hyperbolic lattice point counting, with an appendix by Niko Laaksonen
• The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
• Coefficients of Maass forms and the Siegel zero. Appendix: An effective zero-free region, by Dorian Goldfeld, Jeffrey Hoffstein and Daniel Lieman
• Prime geodesic theorem
• The cubic moment of central values of automorphic \(L\)-functions
• Mean square in the prime geodesic theorem
• Quantum ergodicity of eigenfunctions on \(\text{PSL}_ 2(\mathbb{Z}) \backslash H^ 2\)
• Prime geodesic theorem.
• PETERSSON'S CONJECTURE FOR CUSP FORMS OF WEIGHT ZERO AND LINNIK'S CONJECTURE. SUMS OF KLOOSTERMAN SUMS
• LOCAL AVERAGE OF THE HYPERBOLIC CIRCLE PROBLEM FOR FUCHSIAN GROUPS
• The prime geodesic theorem
• Class numbers of indefinite binary quadratic forms
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