Power partitions and saddle-point method

Power partitions and saddle-point method

For k⩾1, denote by pk(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 pk(n). This approach turns out to significantly simplify those of Wright (1934), Vaughan (2015) and Gaf...

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Veröffentlicht in:Journal of number theory 2019-11, Vol.204, p.435-445
Hauptverfasser: Tenenbaum, Gérald, Wu, Jie, Li, Ya-Li
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Sprache:eng
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Asymptotic estimates
Mathematics
Number Theory
Partitions
Partitions into powers
Saddle-point method
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Wu, Jie
Li, Ya-Li
description For k⩾1, denote by pk(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 pk(n). This approach turns out to significantly simplify those of Wright (1934), Vaughan (2015) and Gafni (2016).
doi_str_mv 10.1016/j.jnt.2019.04.013
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source Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; ScienceDirect Journals (5 years ago - present)
subjects Asymptotic estimates
Mathematics
Number Theory
Partitions
Partitions into powers
Saddle-point method
title Power partitions and saddle-point method
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