On Kuznetsov-Bykovskii's formula of counting prime geodesics

DOI10.1007/s00209-021-02808-5zbMath1486.11082arXiv1901.03824OpenAlexW3184296657MaRDI QIDQ2070958

Han Wu, Giacomo Cherubini, Gergely Zábrádi

Publication date: 25 January 2022

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.03824

zbMATH Keywords

Rankin-Selberg methodprime geodesic theorem

Mathematics Subject Classification ID

Structure of modular groups and generalizations; arithmetic groups (11F06) 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 (2)

Spectral decomposition formula and moments of symmetric square $L$-functions ⋮ Bias of root numbers for Hilbert newforms of cubic level

Cites Work

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• The arithmetic and geometry of some hyperbolic three manifolds
• On the Ramanujan conjecture over number fields
• Die Funktionalgleichungen einiger Dirichletscher Reihen
• On the Kuznetsov-Bruggeman formula for a Hilbert modular surface having one cusp
• Isospectral and non-isometric Riemannian manifolds
• Prime geodesic theorem
• The cubic moment of central values of automorphic \(L\)-functions
• Refined dimensions of cusp forms, and equidistribution and bias of signs
• An explicit trace formula of Jacquet-Zagier type for Hilbert modular forms
• Quantum ergodicity of eigenfunctions on \(\text{PSL}_ 2(\mathbb{Z}) \backslash H^ 2\)
• Prime geodesic theorem for the Picard manifold
• Prime Geodesic Theorem for the Picard manifold under the mean-Lindelöf hypothesis
• Bounds for Rankin–Selberg integrals and quantum unique ergodicity for powerful levels
• Generalized Ramanujan conjecture over general imaginary quadratic fields
• Eisenstein Series and the Selberg Trace Formula. II
• Prime geodesic theorem.
• The Selberg trace formula for the Picard group SL(2, Z[i)]
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• The prime geodesic theorem
• Prime geodesic theorem in the 3-dimensional hyperbolic space
• Deducing Selberg trace formula via Rankin–Selberg method for 𝐺𝐿₂
• Can One Hear the Shape of a Drum?
• Modular Forms
• Weyl's law in the theory of automorphic forms

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