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On Partitions into Powers of Primes and Their Difference Functions |
Canad. J. Math. 61(2009), 465-480
Published:2009-04-01
Printed: Apr 2009
Printed: Apr 2009
- Roger Woodford
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 - Partitions of integers [See also 11P81, 11P82, 11P83] 11P81 - Elementary theory of partitions [See also 05A17] |