Pith. sign in

REVIEW 2 cited by

Power partitions and saddle-point method

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1901.02234 v4 pith:ZOHSYAAZ submitted 2019-01-08 math.NT

Gérald Tenenbaum , Jie Wu , Yali Li This is my paper · ORCID
classification math.NT
keywords methodpartitionssaddle-pointapplyapproachasymptoticdenoteexpansion
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
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).

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The anisotropic chiral boson

    hep-th 2019-09 conditional novelty 7.0 of 10

    An anisotropic (Lifshitz-like) chiral boson has an exact partition function generated by partitions into z-th powers, plus a nonlocal conformal symmetry.

  2. Power Partitions and Hayman Functions

    math.PR 2026-02 unverdicted novelty 6.0 of 10

    The k-th-power partition generating function P_k is strongly Gaussian, recovering the Hardy–Ramanujan asymptotic formula from Hayman's theorem.

Pith tools