Functions of a complex variable Basic notions Concept
Möbius transformation
Summary
A Möbius transformation is a map of the Riemann sphere to itself, with , see the definition. These maps are bijective and holomorphic, they preserve angles, and they map circles and lines to circles and lines.
Where this leads
57 pages build on this one.
- Horocycle flow
- Steinitz's theorem
- Oscillator representation
- Eisenstein series
- Schwarz–Christoffel mapping
- Maass wave form
- Modular lambda function
- Modular curve
- Fuchsian group
- Representation theory of SL2(R)
- Siegel upper half-space
- Geodesic flow on a locally symmetric space
- Theta correspondence
- Theta function
- Kummer's 24 solutions
- Eisenstein series as a double series
- Ramanujan tau function
- Siegel modular form
- Metaplectic group
- Inversive geometry
- Poincaré group
- Riemann P-symbol
- Selberg's 1/4 conjecture
- Arthur–Selberg trace formula
- Selberg trace formula
- Baily–Borel compactification
- Wigner's classification
- Congruence subgroup
- Inoue surface
- Circle packing theorem
- Weyl–Titchmarsh theory
- SL(2,C)
- Ultraparallel theorem
- j-invariant
- Dedekind eta function
- Modular form
- Kleinian group
- Petersson inner product
- Horocycle
- SL(2,R)
- Lorentz group
- Representation theory of the Lorentz group
- Poincaré half-plane model
- Cusp form
- Fundamental domain of the modular group
- Topological modular forms
- Nome
- Modular group
- Rogers–Ramanujan continued fraction
- Schottky group
- Upper half-plane
- Hecke operator
- Theta transformation formula
- Schramm–Loewner evolution
- de Branges space
- Nevanlinna parametrization of solutions
- Loewner differential equation
Further reading
About this page
| Tag | 0SG74WBFA2 |
|---|---|
| URI | m2://0SG74WBFA2 |
| Aliases | mobius-transformation, linear-fractional-transformation, fractional-linear-transformation |
| Kind | concept |
| Writing | W1 stated |
| MSC | 30C35 |
| Specializes | Conformal map |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (1 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
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