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
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic estimates
Mathematics
Number Theory
Partitions
Partitions into powers
Saddle-point method
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Zusammenfassung: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).
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2019.04.013