Prime geodesic theorem in the 3-dimensional hyperbolic space
Artikel i vetenskaplig tidskrift, 2019

For Γ a cofinite Kleinian group acting on H3, we study the prime geodesic theorem on M = Γ\H3, which asks about the asymptotic behavior of lengths of primitive closed geodesics (prime geodesics) on M. Let EΓ(X) be the error in the counting of prime geodesics with length at most log X. For the Picard manifold, Γ = PSL(2, Z[i]), we improve the classical bound of Sarnak, EΓ(X) = O(X5/3+e), to EΓ(X) = O(X13/8+e). In the process we obtain a mean subconvexity estimate for the Rankin-Selberg L-function attached to Maass-Hecke cusp forms. We also investigate the second moment of EΓ(X) for a general cofinite group Γ, and we show that it is bounded by O(X16/5+e).

Prime geodesic theorem

Kloosterman sums

Selberg trace formula

Kuznetsov trace formula

Författare

Olga Balkanova

Chalmers, Matematiska vetenskaper, Algebra och geometri

Dimitrios Chatzakos

Lille I: Universite des Sciences et Technologies de Lille

Giacomo Cherubini

Università degli Studi di Genova

Dmitry Frolenkov

Russian Academy of Sciences

National Research University Higher School of Economics

Niko Laaksonen

McGill University

Transactions of the American Mathematical Society

0002-9947 (ISSN) 1088-6850 (eISSN)

Vol. 372 8 5355-5374

Ämneskategorier

Sannolikhetsteori och statistik

Diskret matematik

Matematisk analys

DOI

10.1090/tran/7720

Mer information

Senast uppdaterat

2020-01-09