• Corpus ID: 102351339

On the asymptotic distinct prime partitions of integers

@article{Murthy2019OnTA,
  title={On the asymptotic distinct prime partitions of integers},
  author={M. V. N. Murthy and Matthias Brack and Rajat Kumar Bhaduri},
  journal={arXiv: Number Theory},
  year={2019}
}
We discuss $Q(n)$, the number of ways a given integer $n$ may be written as a sum of distinct primes, and study its asymptotic form $Q_{as}(n)$ valid in the limit $n\to\infty$. We obtain $Q_{as}(n)$ by Laplace inverting the fermionic partition function of primes, in number theory called the generating function of the distinct prime partitions, in the saddle-point approximation. We find that our result of $Q_{as}(n)$, which includes two higher-order corrections to the leading term in its… 

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