In this paper, we study a certain partition function a（n） defined by ∑n≥0 a（n）qn ：= ∏n=1（1- qn）-1（1 -2n）-1. We prove that given a positive integer j 〉 1 and a prime m _〉 5, there are infinitely many cong...In this paper, we study a certain partition function a（n） defined by ∑n≥0 a（n）qn ：= ∏n=1（1- qn）-1（1 -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 （rood m3）. This work is inspired by Ono＇s ground breaking result in the study of the distribution of the partition function p（n）.展开更多
文摘In this paper, we study a certain partition function a（n） defined by ∑n≥0 a（n）qn ：= ∏n=1（1- qn）-1（1 -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 （rood m3）. This work is inspired by Ono＇s ground breaking result in the study of the distribution of the partition function p（n）.
