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On Partitions into Powers of Primes and Their Difference Functions

  Published:2009-04-01
 Printed: Apr 2009
  • Roger Woodford
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Abstract

In this paper, we extend the approach first outlined by Hardy and Ramanujan for calculating the asymptotic formulae for the number of partitions into $r$-th powers of primes, $p_{\mathbb{P}^{(r)}}(n)$, to include their difference functions. In doing so, we rectify an oversight of said authors, namely that the first difference function is perforce positive for all values of $n$, and include the magnitude of the error term.
MSC Classifications: 05A17, 11P81 show english descriptions Partitions of integers [See also 11P81, 11P82, 11P83]
Elementary theory of partitions [See also 05A17]
05A17 - Partitions of integers [See also 11P81, 11P82, 11P83]
11P81 - Elementary theory of partitions [See also 05A17]
 

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