Abstract
We survey our construction of invariant functions on the real 3-dimensional hyperbolic space ℍ3 for the Whitehead-link-complement group W ⊂ GL 2(ℤ[i]) and for a few groups commensurable with W. We make use of theta functions on the bounded symmetric domain \( \mathbb{D} \) of type I 2,2 and an embedding i : ℍ3 → \( \mathbb{D} \). The quotient spaces of ℍ3 by these groups are realized by these invariant functions. We review classical results on the λ-function, the j-function and theta constants on the upper half space; our construction is based on them.
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© 2007 Birkhäuser Verlag Basel/Switzerland
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Matsumoto, K. (2007). Invariant Functions with Respect to the Whitehead-Link. In: Holzapfel, RP., Uludağ, A.M., Yoshida, M. (eds) Arithmetic and Geometry Around Hypergeometric Functions. Progress in Mathematics, vol 260. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8284-1_9
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DOI: https://doi.org/10.1007/978-3-7643-8284-1_9
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