Log-concavity of the partition function

@article{Desalvo2013LogconcavityOT,
  title={Log-concavity of the partition function},
  author={Stephen Desalvo and Igor Pak},
  journal={The Ramanujan Journal},
  year={2013},
  volume={38},
  pages={61-73}
}
We prove that the partition function $$p(n)$$p(n) is log-concave for all $$n>25$$n>25. We then extend the results to resolve two related conjectures by Chen and one by Sun. The proofs are based on Lehmer’s estimates on the remainders of the Hardy–Ramanujan and the Rademacher series for $$p(n)$$p(n). 

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References

Publications referenced by this paper.
SHOWING 1-10 OF 23 REFERENCES

Recent developments on log-concavity and q-log-concavity of combinatorial polynomials

W.Y.C. Chen
  • In: FPSAC 2010 Conference Talk Slides. http://www.billchen.org/talks/2010-FPSAC.pdf
  • 2010
VIEW 15 EXCERPTS
HIGHLY INFLUENTIAL

On the series for the partition function

VIEW 11 EXCERPTS
HIGHLY INFLUENTIAL