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15 June 2008 A sum formula for a pair of closed geodesics on a hyperbolic surface
Nigel J. E. Pitt
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Duke Math. J. 143(3): 407-435 (15 June 2008). DOI: 10.1215/00127094-2008-024

Abstract

We consider an arbitrary pair of closed geodesics and the corresponding period integrals for the eigenfunctions of the Laplacian on a compact hyperbolic surface. A summation formula that relates geometric information about the geodesics (namely, the angles of intersection and lengths of common perpendiculars between them) to the period integrals is proved. As a corollary, an asymptotic is obtained for the second moment of the period integrals for a fixed geodesic as an average over the eigenvalue with an error term that can be interpreted in terms of the geometric data

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Nigel J. E. Pitt. "A sum formula for a pair of closed geodesics on a hyperbolic surface." Duke Math. J. 143 (3) 407 - 435, 15 June 2008. https://doi.org/10.1215/00127094-2008-024

Information

Published: 15 June 2008
First available in Project Euclid: 3 June 2008

zbMATH: 1195.11073
MathSciNet: MR2423758
Digital Object Identifier: 10.1215/00127094-2008-024

Subjects:
Primary: 11F67 , 11F72

Rights: Copyright © 2008 Duke University Press

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Vol.143 • No. 3 • 15 June 2008
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