Abstract
Ramanujan's famous congruences for the partition function modulo powers of 5, 7, and 11 have inspired much further research. For example, in 2002 Lovejoy and Ono found subprogressions of 5jn + β5(j) for which Ramanujan's congruence mod 5j could be strengthened to a statement modulo 5j+1. Here we provide the analogous results modulo powers of 7 and 11. We require the arithmetic properties of two special elliptic curves.
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