Power partitions and saddle-point method

Gérald Tenenbaum; Jie Wu; Yali Li

Power partitions and saddle-point method

Number Theory 2019-10-08 v4

Authors: Gérald Tenenbaum , Jie Wu , Yali Li

Abstract

For $k\geqslant 1$ , denote by $p_k(n)$ the number of partitions of an integer $n$ into $k$ -th powers. In this note, we apply the saddle-point method to provide a new proof for the well-known asymptotic expansion of $p_k(n)$ . This approach turns out to significantly simplify those of Wright (1934), Vaughan (2015) and Gafni (2016).

Keywords

partition theory divisor function

Cite

@article{arxiv.1901.02234,
  title  = {Power partitions and saddle-point method},
  author = {Gérald Tenenbaum and Jie Wu and Yali Li},
  journal= {arXiv preprint arXiv:1901.02234},
  year   = {2019}
}

Comments

An error in the proof of Lemma 2.3 has been corrected

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