Partitions into Piatetski-Shapiro sequences

Nian Hong Zhou; Ya-Li Li

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arXiv · 2104.01886

Partitions into Piatetski-Shapiro sequences

Nian Hong Zhou·Ya-Li Li

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Abstract

Let $\kappa$ be a positive real number and $m\in\mathbb{N}\cup\{\infty\}$ be given. Let $p_{\kappa, m}(n)$ denote the number of partitions of $n$ into the parts from the Piatestki-Shapiro sequence $(\lfloor \ell^{\kappa}\rfloor)_{\ell\in \mathbb{N}}$ with at most $m$ times (repetition allowed). In this paper we establish asymptotic formulas of Hardy-Ramanujan type for $p_{\kappa, m}(n)$, by employing a framework of asymptotics of partitions established by Roth-Szekeres in 1953, as well as some results on equidistribution.

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Nian Hong Zhou, Ya-Li Li. 2021-04-05. Partitions into Piatetski-Shapiro sequences. https://arxiv.org/abs/2104.01886

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