On the number of partitions into primes

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)109-121
Number of pages13
JournalRamanujan Journal
Volume15
Issue number1
DOIs
StatePublished - Jan 1 2008

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Logarithmic integral
Partition
Distribution of Primes
Elementary Functions
Asymptotic Formula
Riemann zeta function
Monotonic
Zero
Term
Knowledge
Beliefs

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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On the number of partitions into primes. / Vaughan, Robert Charles.

In: Ramanujan Journal, Vol. 15, No. 1, 01.01.2008, p. 109-121.

Research output: Contribution to journalArticle

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