On the number of partitions into primes

R. C. Vaughan

doi:10.1007/s11139-007-9037-5

On the number of partitions into primes

R. C. Vaughan

Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

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 language	English (US)
Pages (from-to)	109-121
Number of pages	13
Journal	Ramanujan Journal
Volume	15
Issue number	1
DOIs	https://doi.org/10.1007/s11139-007-9037-5
State	Published - Jan 2008

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1007/s11139-007-9037-5

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AB - 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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On the number of partitions into primes

Abstract

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