On the mean average of integer partition as the sum of powers

Pengyong Ding

On the mean average of integer partition as the sum of powers

Number Theory 2022-11-22 v1

Authors: Pengyong Ding

Abstract

This paper is concerned with the function $r_{k,s}(n)$ , the number of (ordered) representations of $n$ as the sum of $s$ positive $k$ -th powers, where integers $k,s\ge 2$ . We examine the mean average of the function, or equivalently, \begin{equation*} \sum_{m=1}^n r_{k,s}(m). \end{equation*}

Keywords

integer partition sum of powers waring problem mean average representation function

Cite

@article{arxiv.2211.10621,
  title  = {On the mean average of integer partition as the sum of powers},
  author = {Pengyong Ding},
  journal= {arXiv preprint arXiv:2211.10621},
  year   = {2022}
}

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