On the number of partitions into primes

There is, apparently, a persistent belief that in the current state of knowledge it is not possible to obtain an asymptotic formula for the number of partitions of a number n into primes when n is large. In this paper such a formula is obtained. Since the distribution of primes can only be described accurately by the use of the logarithmic integral and a sum over zeros of the Riemann zeta-function one cannot expect the main term to involve only elementary functions. However the formula obtained, when n is replaced by a real variable, is in C∞ and is readily seen to be monotonic.



Work Title On the number of partitions into primes
Open Access
  1. R. C. Vaughan
License In Copyright (Rights Reserved)
Work Type Article
  1. Ramanujan Journal
Publication Date January 1, 2008
Publisher Identifier (DOI)
  1. https://doi.org/10.1007/s11139-007-9037-5
Deposited November 17, 2021




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