Proof of Ramanujan’s partition congruence for the modulus 11³

Presented to the Society, October 30, 1948; received by the editors September 13, 1948 and, in revised form, February 9, 1949. 1 The author is greatly indebted to the referee, who made a very careful review of the paper, correcting some errors and elarifying a number of ambiguities. He also supplied footnote 2. 2Actually p can be given explicitly. It is (23. 111+1)/24 for a even and (13* 11 +1)/24 for a odd. 3 Cf. footnotes 2 and 5 in J. Lehner, Ramanujan identities involving the partition function for the moduli IIa, Amer. J. Math. (1943) pp. 492-520. This paper will be referred to hereafter as I.