A Formula for Ramanujan's Tau Function
Copyright policy )A Formula for Ramanujan's Tau Function
A formula for Ramanujan’s tau function τ \tau , defined by ∑ 1 ∞ τ ( n ) x n = x ∏ 1 ∞ ( 1 − x n ) 24 ( | x | > 1 ) \sum \nolimits _1^\infty {\tau (n){x^n} = } x\prod _1^\infty {(1 - {x^n})^{24}}(\left | x \right | > 1) , is presented. The author then observes that some of the known congruence properties of τ \tau are immediate consequences of this formula representation.
arithmetical identity, congruence properties, Ramanujan tau-function, Holomorphic modular forms of integral weight, product of two power series
arithmetical identity, congruence properties, Ramanujan tau-function, Holomorphic modular forms of integral weight, product of two power series
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