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.
|On the number of partitions into primes
|In Copyright (Rights Reserved)
|January 1, 2008
|Publisher Identifier (DOI)
|November 17, 2021
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