Modular lambda function: Difference between revisions

Revision as of 16:52, 27 August 2021

Revision as of 15:28, 28 August 2021

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The values of λ*(x) can be computed as follows:

:<math>\lambda^*(x) = \frac{\varthetatheta^2_2[(0;\exp(-\pi,i\sqrt{x})]}{\varthetatheta^2_3[(0;\exp(-\pi,i\sqrt{x})]} </math>

:<math>\lambda^*(x) = \left[\sum_{a=-\infty}^\infty\exp[-(a+1/2)^2\pi\sqrt{x}]\right]^2\left[\sum_{a=-\infty}^\infty\exp(-a^2\pi\sqrt{x})\right]^{-2} </math>