The authors construct (∞:∞) holomorphic correspondences mating transcendental entire maps with Fuchsian groups, realized as deleted covering correspondences of meromorphic functions with one simple pole.
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Algebraic correspondences exist that combine Fuchsian (p,q,∞)-triangle groups with Blaschke products B1=β2,1∘β1,2 and B2=β1,2∘β2,1 of degrees (p-1)(q-1) fixing 0 and 1.
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Transcendental correspondences: when Fuchsian groups take over basins of entire maps
The authors construct (∞:∞) holomorphic correspondences mating transcendental entire maps with Fuchsian groups, realized as deleted covering correspondences of meromorphic functions with one simple pole.
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Combining cusped triangle groups with Blaschke products: commensurable matings
Algebraic correspondences exist that combine Fuchsian (p,q,∞)-triangle groups with Blaschke products B1=β2,1∘β1,2 and B2=β1,2∘β2,1 of degrees (p-1)(q-1) fixing 0 and 1.