English

Asymptotics and inequalities for partitions into squares

Number Theory 2019-10-02 v2

Abstract

In this paper we prove that the number of partitions into squares with an even number of parts is asymptotically equal to that of partitions into squares with an odd number of parts. We further show that, for n n large enough, the two quantities are different and which of the two is bigger depends on the parity of n. n. This solves a recent conjecture formulated by Bringmann and Mahlburg (2012).

Keywords

Cite

@article{arxiv.1806.00708,
  title  = {Asymptotics and inequalities for partitions into squares},
  author = {Alexandru Ciolan},
  journal= {arXiv preprint arXiv:1806.00708},
  year   = {2019}
}

Comments

17 pages; accepted in Int. J. Number Theory, online ready

R2 v1 2026-06-23T02:17:06.943Z