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Titus Piezas III science forum Guru Wannabe
Joined: 10 Mar 2005
Posts: 102

Posted: Thu Jun 15, 2006 9:28 am Post subject:
Curious properties of jfunction formulas



Hello all,
The approximation,
e^(Pi*Sqrt[163]) = 640302^3 + 743.99999999999925...
is well known, with 640320^3 an exact value of the jfunction j(tau).
This function turns out to have defining formulas that are also
interesting. If expressed in the form j(tau) = f(x)/g(x) for some
polynomials in terms of a function x, and defining the expression
S = Numerator + 1728Denominator
then S is a square or a nearsquare. The question is Why? Details at,
www.geocities.com/titus_piezas/ramanujan_page17.html
(Contains only a pdf file.)
Titus 

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