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A note on the McShane’s identity for Hecke groups

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An Erratum to this article was published on 05 August 2021

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Abstract

The generalization of McShane’s identity for the quotient surface \(\Sigma_q\) of any Hecke group \(H_q\), where q is an integer greater than 3.

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References

  1. A. Beardon, The geometry of discrete groups, Springer-Verlag, New York 1983.

    Book  Google Scholar 

  2. J. Birman, C. Series, An algorithm for simple curves on surfaces, J. London Math. Soc. (2) 29 (1984), 331-342.

  3. K. Farooq, The structural properties of quotient surfaces of a Hecke group, Conform. Geom. Dyn. 23 (2019), 262-282.

    Article  MathSciNet  Google Scholar 

  4. G. McShane, A remarkable identity for the length of curves on surfaces, - Ph.D. thesis, University of Warwick, 1991.

  5. G. McShane, Simple geodesics and a series constant over Teichmuller space, Invent. Math. 132 (1998) 607-632.

    Article  MathSciNet  Google Scholar 

  6. G. McShane, Weierstrass points and simple geodesics, Bull. London Math. Soc. 36 (2004) 181-187.

    Article  MathSciNet  Google Scholar 

  7. G. McShane, Simple geodesics on surfaces of genus two, Annales Academi Scientiarum Fennic 31 (2006) 31-38

    MathSciNet  MATH  Google Scholar 

  8. A. Haas, The geometry of the hyperelliptic involution in genus two, Proceedings of Amer. Math. Soc. (1) 105 (1989) 159-165.

  9. S.P. Tan, Y.L. Wong & Y. Zhang, Generalisation of McShane’s identity to hyperbolic cone-surfaces, J. Differential Geom. 72 (2006) 73-112.

    Article  MathSciNet  Google Scholar 

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Correspondence to K. Farooq.

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Communicated by Gadadhar Misra.

The original online version of this article was revised due to an error in Theorem A.

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Farooq, K. A note on the McShane’s identity for Hecke groups. Indian J Pure Appl Math 52, 915–931 (2021). https://doi.org/10.1007/s13226-021-00043-6

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  • DOI: https://doi.org/10.1007/s13226-021-00043-6

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