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Prime geodesic theo...
Prime geodesic theorem in the 3-dimensional hyperbolic space
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- Balkanova, Olga, 1988 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences
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- Chatzakos, Dimitrios (author)
- Lille I: Universite des Sciences et Technologies de Lille (USTL),Lille 1 University of Science and Technology (USTL)
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- Cherubini, Giacomo (author)
- Università degli Studi di Genova,University of Genoa
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- Frolenkov, Dmitry (author)
- National Research University Higher School of Economics,Russian Academy of Sciences
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- Laaksonen, Niko (author)
- McGill University
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(creator_code:org_t)
- 2018-12-28
- 2019
- English.
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In: Transactions of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9947 .- 1088-6850. ; 372:8, s. 5355-5374
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Abstract
Subject headings
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- 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).
Subject headings
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Diskret matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Discrete Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- Kloosterman sums
- Selberg trace formula
- Kuznetsov trace formula
- Prime geodesic theorem
- Kloosterman sums
- Kuznetsov trace formula
- Prime geodesic theorem
- Selberg trace formula
Publication and Content Type
- art (subject category)
- ref (subject category)
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