• Corpus ID: 16000436

Distribution of the partition function modulo m

@inproceedings{Ono2001DistributionOT,
  title={Distribution of the partition function modulo m},
  author={Ken Ono},
  year={2001}
}
  • K. Ono
  • Published 2001
  • Mathematics
and he conjectured further such congruences modulo arbitrary powers of 5, 7, and 11. Although the work of A. O. L. Atkin and G. N. Watson settled these conjectures many years ago, the congruences have continued to attract much attention. For example, subsequent works by G. Andrews, A. O. L. Atkin, F. Garvan, D. Kim, D. Stanton, and H. P. F. Swinnerton-Dyer ([An-G], [G], [G-K-S], [At-Sw2]), in the spirit of F. Dyson, have gone a long way towards providing combinatorial and physical explanations… 
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References

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has infinitely many solutions in non-negative integers n. This conjecture seems difficult and I have only scattered results. In ?2 of this paper it will be shown that the conjecture is true for m= 5
SOME PROPERTIES OF p(n) AND c(n) MODULO POWERS OF 13
j(^r) = E c(n)xn = (1 +240 0 u3(n)xn) /xf24(x) 744, where 03(n) = d3. dln Then p(n) is just the number of unrestricted partitions of n, and c(n) is the Fourier coefficient of Klein's modular
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If n is a non-negative integer, define p r(n) as the coefficient of x n in ; otherwise define p r(n) as 0. In a recent paper (2) the author established the following congruence: Let r = 4, 6, 8, 10,
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When Ramanujan died in 1920, he left behind an incomplete, unpublished manuscript in two parts on the partition function p(n) and, in contemporary terminology, Ramanujan’s tau-function τ(n). The
On the Parity of Additive Representation Functions
Abstract Let A be a set of positive integers,p( A , n) be the number of partitions ofnwith parts in A , andp(n)=p(N, n). It is proved that the number ofn⩽Nfor whichp(n) is even is ⪢ N , while the
CRANKS AND t-CORES
New statistics on partitions (called cranks) are defined which combinatorially prove Ramanujan’s congruences for the partition function modulo 5, 7, 11, and 25. Explicit bijections are given for the
Ramanujan’s Unpublished Manuscript on the Partition and Tau Functions with Proofs and Commentary
When Ramanujan died in 1920, he left behind an incomplete, unpublished manuscript in two parts on the partition function p(n) and, in contemporary terminology, Ramanujan’s tau-function τ(n). The
Modular forms of weight 1/2
We will construct θ-series of weight 1/2 and 3/2 for some congruence subgroups of SL(2,ℤ) by taking appropriate coefficients of the representation \( \mathop{R}\limits^{\sim } \) of SL(2;ℝ),
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