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July 2014 An infinite product associated to a hyperbolic three-holed sphere
Toshihiro Nakanishi
Hiroshima Math. J. 44(2): 157-172 (July 2014). DOI: 10.32917/hmj/1408972905


One of the generalizations of McShane’s identities by Tan, Wong and Zhang is an identity concerning lengths of simple closed geodesics which pass through two Weierstrass points on a hyperbolic one-holed torus. The Fuchsian groups which uniformize the surface are purely hyperbolic and free of rank two. Another type of Fuchsian groups of the same property is of type (0, 3) corresponding to hyperbolic three-holed spheres. In this paper we show a McShane-type identity which holds for all Fuchsian groups of type (0, 3).


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Toshihiro Nakanishi. "An infinite product associated to a hyperbolic three-holed sphere." Hiroshima Math. J. 44 (2) 157 - 172, July 2014.


Published: July 2014
First available in Project Euclid: 25 August 2014

zbMATH: 1300.30080
MathSciNet: MR3251820
Digital Object Identifier: 10.32917/hmj/1408972905

Rights: Copyright © 2014 Hiroshima University, Mathematics Program


Vol.44 • No. 2 • July 2014
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