On the Parity of the Number of Partitions in Square Free Parts
Part of the Developments in Mathematics book series (DEVM, volume 10)
Let \( \tilde p(n) \) be the number of partitions of a positive integer n in square free parts. We prove that for large N,
The number of n ≤ N such that \( \tilde p(n) \) is odd is ≫ log N
The number of n ≤ N such that \( \tilde p(n) \) is even is ≫ N/log N.
Key wordspartition function parity problem square free numbers
Unable to display preview. Download preview PDF.
- 3.G.H. Hardy and S. Ramanujan, “Asymptotic formulae for the distribution of integers of various types,” Proc. London Math. Soc. 16 (1917), 112–132.Google Scholar
© Springer Science+Business Media New York 2003