Improved asymptotics for moments of reciprocal sums for partitions into distinct parts

Kathrin Bringmann; Byungchan Kim; Eunmi Kim

doi:10.1016/j.jcta.2025.106119

Improved asymptotics for moments of reciprocal sums for partitions into distinct parts

Kathrin Bringmann
, Byungchan Kim
, Eunmi Kim

School of Natural Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we strongly improve asymptotics for s₁(n) (respectively s₂(n)) which sums reciprocals (respectively squares of reciprocals) of parts throughout all the partitions of n into distinct parts. The methods required are much more involved than in the case of usual partitions since the generating functions are not modular and also do not possess product expansions.

Original language	English
Article number	106119
Journal	Journal of Combinatorial Theory. Series A
Volume	219
DOIs	https://doi.org/10.1016/j.jcta.2025.106119
State	Published - Apr 2026

Keywords

Asymptotics
Circle method
Partitions

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10.1016/j.jcta.2025.106119

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title = "Improved asymptotics for moments of reciprocal sums for partitions into distinct parts",

abstract = "In this paper we strongly improve asymptotics for s1(n) (respectively s2(n)) which sums reciprocals (respectively squares of reciprocals) of parts throughout all the partitions of n into distinct parts. The methods required are much more involved than in the case of usual partitions since the generating functions are not modular and also do not possess product expansions.",

keywords = "Asymptotics, Circle method, Partitions",

author = "Kathrin Bringmann and Byungchan Kim and Eunmi Kim",

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year = "2026",

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doi = "10.1016/j.jcta.2025.106119",

language = "English",

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AU - Bringmann, Kathrin

AU - Kim, Byungchan

AU - Kim, Eunmi

PY - 2026/4

Y1 - 2026/4

N2 - In this paper we strongly improve asymptotics for s1(n) (respectively s2(n)) which sums reciprocals (respectively squares of reciprocals) of parts throughout all the partitions of n into distinct parts. The methods required are much more involved than in the case of usual partitions since the generating functions are not modular and also do not possess product expansions.

AB - In this paper we strongly improve asymptotics for s1(n) (respectively s2(n)) which sums reciprocals (respectively squares of reciprocals) of parts throughout all the partitions of n into distinct parts. The methods required are much more involved than in the case of usual partitions since the generating functions are not modular and also do not possess product expansions.

KW - Asymptotics

KW - Circle method

KW - Partitions

UR - https://www.scopus.com/pages/publications/105017018884

U2 - 10.1016/j.jcta.2025.106119

DO - 10.1016/j.jcta.2025.106119

M3 - Article

AN - SCOPUS:105017018884

SN - 0097-3165

VL - 219

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

M1 - 106119

ER -

Improved asymptotics for moments of reciprocal sums for partitions into distinct parts

Abstract

Keywords

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