Difference between revisions of "Klein invariant J"
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| − | The Klein j-invariant $j(\tau)$ is ''the'' modular function which encodes arithmetic information about the singular moduli of imaginary quadratic fields. | + | [[File:kleinj.png|700px]] |
| − | It is invariant under the full modular group $\mathbf{SL}(2,\mathbb{Z})$ | + | |
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| + | The Klein j-invariant $j(\tau)$ is ''the'' [[modular function]] which encodes arithmetic information about the [[singular moduli]] of [[imaginary quadratic fields]]. | ||
| + | It is invariant under the [[full modular group]] $\mathbf{SL}(2,\mathbb{Z})$. | ||
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| + | =Videos= | ||
| + | [https://www.youtube.com/watch?v=kvQ7e2AiE2g Klein's j-Invariant j(τ) under τ→-1/τ in SL(2,R)] | ||
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| + | [[Category:SpecialFunction]] | ||
Latest revision as of 18:28, 24 May 2016
The Klein j-invariant $j(\tau)$ is the modular function which encodes arithmetic information about the singular moduli of imaginary quadratic fields.
It is invariant under the full modular group $\mathbf{SL}(2,\mathbb{Z})$.
