Abstract
Let NT(m,k,n) denote the total number of parts in the partitions of n with rank congruent to m modulo k. Andrews recently provided a q-series proof of congruences for NT(m,k,n) modulo 5 and 7. In this paper, we establish congruences for NT(m,k,n) modulo powers of primes ℓ≥7. Our proof utilizes the Hecke operators.
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