Prime geodesic theorem.

DOI10.1515/crll.1984.349.136zbMath0527.10021OpenAlexW4234295474MaRDI QIDQ3043235

Henryk Iwaniec

Publication date: 1984

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://www.digizeitschriften.de/dms/resolveppn/?PPN=GDZPPN002201410

zbMATH Keywords

Selberg trace formulaerror termSelberg zeta-functionfull modular grouplengths of closed geodesicspseudoprimesclasses of binary indefinite quadratic formsnumber of primitive hyperbolic classessums of sums of Kloosterman sums

Mathematics Subject Classification ID

Asymptotic results on counting functions for algebraic and topological structures (11N45) Geodesics in global differential geometry (53C22) Gauss and Kloosterman sums; generalizations (11L05) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Holomorphic modular forms of integral weight (11F11) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

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