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]].
 
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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It is invariant under the [[full modular group]] $\mathbf{SL}(2,\mathbb{Z})$.
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=Videos=
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[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

Kleinj.png


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 $\mathbf{SL}(2,\mathbb{Z})$.

Videos

Klein's j-Invariant j(τ) under τ→-1/τ in SL(2,R)