Abstract
In this paper, we study a certain partition function a(n) defined by Σn≥0 a(n)q n:= Πn=1(1 − q n)−1(1 − q 2n)−1. We prove that given a positive integer j ≥ 1 and a prime m ≥ 5, there are infinitely many congruences of the type a(An + B) ≡ 0 (mod m j). This work is inspired by Ono’s ground breaking result in the study of the distribution of the partition function p(n).
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Chan, HC. Distribution of a certain partition function modulo powers of primes. Acta. Math. Sin.-English Ser. 27, 625–634 (2011). https://doi.org/10.1007/s10114-011-8620-2
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DOI: https://doi.org/10.1007/s10114-011-8620-2