Mean square in the prime geodesic theorem

DOI10.2140/ant.2018.12.571zbMath1422.11122arXiv1702.00297OpenAlexW2583646051WikidataQ129723549 ScholiaQ129723549MaRDI QIDQ1643327

Giacomo Cherubini, João Nisan C. Guerreiro

Publication date: 19 June 2018

Published in: Algebra \& Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.00297

zbMATH Keywords

Selberg trace formulaKloosterman sumsKuznetsov trace formulaprime geodesic theorem

Mathematics Subject Classification ID

Gauss and Kloosterman sums; generalizations (11L05) 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 (9)

Gallagherian \(PGT\) on \(\mathrm{PSL}(2,\mathbb{Z})\) ⋮ Prime geodesics and averages of the Zagier L-series ⋮ Gallagherian prime geodesic theorem in higher dimensions ⋮ The prime geodesic theorem in square mean ⋮ Bounds for a spectral exponential sum ⋮ 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 \(\mathrm{PSL}(2, \mathbb{Z}[i)\)] ⋮ Prime geodesic theorem in the 3-dimensional hyperbolic space

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