Curious properties of j-function formulas

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

Hello all,

It seem the j-function j(tau) has 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. Now why is that? Formulas in
terms of continued fractions will also be given. Details at,

http://www.geocities.com/titus_piezas/ramanujan_page17.html

(A pdf file inside.)

--Titus

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