A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is
A REFINEMENT OF RAMANUJAN'S CONGRUENCES MODULO POWERS OF 7 AND 11
International Journal of Number Theory
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 5 j n + β 5 (j) for which Ramanujan's congruence mod 5 j could be strengthened to a statement modulo 5 j+1 . Here we provide the analogous results modulo powers of 7 and 11. We require the arithmetic properties of two special elliptic curves.doi:10.1142/s1793042112500510 fatcat:tdjdojmysrdvbod4bnerzyxpfm