- the sum is over all simple closed geodesics γ on the torus; and
- ℓ(γ) denotes the hyperbolic length of γ.
- Necessary and Sufficient Conditions for McShane's Identity and Variations Ser Peow Tan, Yan Loi Wong, and Ying Zhang eprint arXiv:math/0411184 
- McShane, G. Simple geodesics and a series constant over Teichmuller space. Invent. Math. 132 (1998), no. 3, 607–632.