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.

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Work Title On the number of partitions into primes
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Open Access
Creators
  1. R. C. Vaughan
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  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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