Modular lambda function: Difference between revisions

Revision as of 13:23, 4 May 2021

Revision as of 10:13, 6 May 2021

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:<math>a^{8}+b^{8}-7a^4b^4 = 2\sqrt{2}ab+2\sqrt{2}a^7b^7\, \left(a = \left[\frac{2\lambda^*(x)}{1-\lambda^*(x)^2}\right]^{1/12}\right) \left(b = \left[\frac{2\lambda^*(49x)}{1-\lambda^*(49x)^2}\right]^{1/12}\right) </math>

:<math>a^{12}-c^{12} = 42\sqrt{2}(ac+22\sqrt{2}a^3c^3)(1+44\sqrt{2}a3a^5c2c^52+44\sqrt{2}a^7c4c^74)(2+22\sqrt{2}a3a^9c2c^92+4\sqrt{2}a2a^{11}c4c^{11}4)\, \left(a = \left[\frac{2\lambda^*(x)}{1-\lambda^*(x)^2}\right]^{1/12}\right) \left(c = \left[\frac{2\lambda^*(121x)}{1-\lambda^*(121x)^2}\right]^{1/12}\right) </math>

:<math>(a^2-d^2)(a^4+d^4-7a^2d^2)[(a^2-d^2)^4-a^2d^2(a^2+d^2)^2] = 8ad+8a^{13}d^{13}\, \left(a = \left[\frac{2\lambda^*(x)}{1-\lambda^*(x)^2}\right]^{1/12}\right) \left(d = \left[\frac{2\lambda^*(169x)}{1-\lambda^*(169x)^2}\right]^{1/12}\right) </math>