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tau.m

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19 May 2004 (Updated )

Given a nonnegative integer n, tau(n) is the Ramanujan tau function of n.

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Description

Given a nonnegative integer n, tau(n) is the Ramanujan tau function of n, defined as the coefficient of x^n in the Taylor expansion of
x * prod_{k>=0}(1 - x^k)^24. This is an integer function with fascinating number theoretic properties. For instance, it's multiplicative, meaning tau(m*n) = tau(m)*tau(n) for m and n coprime. It also satisfies some unusual modular properties, like
tau(n) - sigma_11(n) is always divisible by 691. It's also important in the study of elliptic curves and modular forms.

Required Products Bioinformatics Toolbox
MATLAB release MATLAB 6.0 (R12)
Other requirements requires first downloading factor2.m and sigma.m
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