Distribution of the partition function modulo $m$

  title={Distribution of the partition function modulo \$m\$},
  author={Ken Ono},
  journal={Annals of Mathematics},
  • K. Ono
  • Published 17 August 2000
  • Mathematics
  • Annals of Mathematics
Ramanujan (and others) proved that the partition function satisfies a number of striking congruences modulo powers of 5, 7 and 11. A number of further congruences were shown by the works of Atkin, O'Brien, and Newman. In this paper we prove that there are infinitely many such congruences for every prime modulus exceeding 3. In addition, we provide a simple criterion guaranteeing the truth of Newman's conjecture for any prime modulus exceeding 3 (recall that Newman's conjecture asserts that the… 
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  • Mathematics
    Proceedings of the National Academy of Sciences
  • 2008
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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
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  • M. Newman
  • Mathematics
    Canadian Journal of Mathematics
  • 1957
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