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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 j-function formulas

Hello all,

The approximation,

e^(Pi*Sqrt[163]) = 640302^3 + 743.99999999999925...

is well known, with -640320^3 an exact value of the j-function 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 near-square. The question is Why? Details at,

www.geocities.com/titus_piezas/ramanujan_page17.html

(Contains only a pdf file.)

--Titus

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