On some claims in Ramanujan's 'unpublished' manuscript on the partition and tau functions

摘要

We disprove various claims made by Ramanujan in his, until very recently, unpublished manuscript (Berndt and Ono, The Andrews Festschrift, (D. Foata and G.N. Han, Eds. (2001, 39-110) on the partition and tau functions. Furthermore, the second part of a related paper by G.K. Stanley (Journal London Math. Soc. 3 (1928), 232-237) is corrected (the first part of which was earlier corrected by D. Shanks (Math. Comp. 18 (1964),75-86)).