Algebra & Number Theory

Mean square in the prime geodesic theorem

Giacomo Cherubini and João Guerreiro

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Abstract

We prove upper bounds for the mean square of the remainder in the prime geodesic theorem, for every cofinite Fuchsian group, which improve on average on the best known pointwise bounds. The proof relies on the Selberg trace formula. For the modular group we prove a refined upper bound by using the Kuznetsov trace formula.

Article information

Source
Algebra Number Theory, Volume 12, Number 3 (2018), 571-597.

Dates
Received: 23 May 2017
Revised: 26 October 2017
Accepted: 30 December 2017
First available in Project Euclid: 28 July 2018

Permanent link to this document
https://projecteuclid.org/euclid.ant/1532743365

Digital Object Identifier
doi:10.2140/ant.2018.12.571

Mathematical Reviews number (MathSciNet)
MR3815307

Zentralblatt MATH identifier
06890762

Subjects
Primary: 11F72: Spectral theory; Selberg trace formula
Secondary: 11L05: Gauss and Kloosterman sums; generalizations 11M36: Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas

Keywords
prime geodesic theorem Selberg trace formula Kuznetsov trace formula Kloosterman sums

Citation

Cherubini, Giacomo; Guerreiro, João. Mean square in the prime geodesic theorem. Algebra Number Theory 12 (2018), no. 3, 571--597. doi:10.2140/ant.2018.12.571. https://projecteuclid.org/euclid.ant/1532743365


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