Erratum to: The Ramanujan τ-Function

The online version of the original chapter can be found at doi: 10.1007/978-81-322-0770-2_2.

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Erratum to: M.R. Murty, V.K. Murty, The Mathematical Legacy of Srinivasa Ramanujan , pp. 11–23, DOI 10.1007/978-81-322-0770-2_2 , © Springer India 2013

Page 17: The third displayed equation should be a congruence (mod 2). It is clearer if we note (1−q ⁿ)²⁴≡(1−q ⁸ⁿ)³ (mod 2) and observe that

$$\prod^{\infty}_{n=1} \bigl(1 - q^{8n}\bigr)^3 = \sum^{\infty}_{m=0} (-1)^m(2m + 1)q^{4m^2+4m} \equiv q^{4m^2+4m} \quad (\mathrm{mod}\ 2). $$