Distribution of a certain partition function modulo powers of primes |
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Authors: | Hei-Chi Chan |
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Affiliation: | Department of Mathematical Sciences, University of Illinois at Springfield, Springfield, IL 62703-5407, USA |
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Abstract: | In this paper, we study a certain partition function a(n) defined by Σ n≥0 a(n)q n := Π n=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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Keywords: | Distribution of partition function Ono's theorem Ramanujan's congruences |
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