tau.m
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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.
引用
David Terr (2024). tau.m (https://www.mathworks.com/matlabcentral/fileexchange/4968-tau-m), MATLAB Central File Exchange. 取得済み .
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1.0.0.0 | I updated this file so that it works with my update of factor2.m and fixed a bug involving printout of intermediate results. |