j-invariant
Also known as modular j-invariant, J-invariant function
right|thumb|200px|Klein's -invariant in the complex plane
~16 min read
Article
15 sectionsContents
- Definition
- The fundamental region
- Class field theory and {{mvar|''j''}}
- Transcendence properties
- The {{mvar|q}}-expansion and moonshine
- Moonshine
- Alternate expressions
- Expressions in terms of theta functions
- Algebraic definition
- Inverse function
- Pi formulas
- Failure to classify elliptic curves over other fields
- References
- Notes
- Other
right|thumb|200px|Klein's -invariant in the complex plane
In mathematics, the -invariant or function is a modular function of weight zero for the special linear group \operatorname{SL}(2,\Z) defined on the upper half-plane of complex numbers. It is the unique such function that is holomorphic away from a simple pole at the cusp such that