# The partition function and Hecke operators

@article{Ono2011ThePF,
title={The partition function and Hecke operators},
author={Ken Ono},
year={2011},
volume={228},
pages={527-534}
}
• K. Ono
• Published 10 September 2011
• Mathematics
1 Citations
Hecke-type congruences for Andrews' spt-function modulo 16 and 32
• Mathematics
• 2013
Inspired by recent congruences by Andersen with varying powers of 2 in the modulus for partition related functions, we extend the modulo 32760 congruences of the first author for the function spt(n).

## References

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Let p(n) denote the partition function. In this article, we will show that congruences of the formexist for all primes m and l satisfying m≥13 and l≠2,3,m, where B is a suitably chosen integer
Congruence properties for the partition function
• Mathematics
Proceedings of the National Academy of Sciences of the United States of America
• 2001
It is reported that such congruences are much more widespread than was previously known, and the theoretical framework that appears to explain every known Ramanujan-type congruence is described.
Zeros of certain modular functions and an application
• Mathematics
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As has been known since the work of F.K.C. Rankin and H.P.F. Swinnerton-Dyer [8], the values of j(τ) at the zeros in H of the Eisenstein series Ek(τ) of any weight k on SL2(Z) always lie in the
New Congruences for the Partition Function
AbstractLet p(n) denote the number of unrestricted partitions of a non-negative integer n. In 1919, Ramanujan proved that for every non-negative n \begin{gathered} p(5 + 4) \equiv 0(\bmod 5),
Distribution of the partition function modulo composite integers M
seem to be distinguished by the fact that they are exceptionally rare. Recently, Ono [O1] has gone some way towards quantifying the latter assertion. More recently, Ono [O2] has made great progress
SOME PROPERTIES OF p(n) AND c(n) MODULO POWERS OF 13
• Mathematics
• 1967
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
Proof of a conjecture of Ramanujan
• A. Atkin
• Mathematics
Glasgow Mathematical Journal
• 1967
We write and so that p(n) is the number of unrestricted partitions of n. Ramanujan [1] conjectured in 1919 that if q = 5, 7, or 11, and 24m ≡ 1 (mod qn), then p(m) ≡ 0 (mod qn). He proved his