On Ramanujan's tau function
Ramanujan's function \(\tau(n)\) is defined by \[ \sum_1^\infty \tau(n) x^n= x\prod_1^\infty (1-x^n)^{24}, \qquad |x|<1. \] The author gives a new representation of \(\tau(n)\), which contains finite sums of values of \(\sigma_3\) (3rd powers divisor function) and \(r_8\) (number of sums of 8 squares). He deduces a congruence \(\operatorname {mod}16\) of \(\tau(n)\).
scientific article; zbMATH DE number 1309725
scientific article