Modularity of moments of reciprocal sums for partitions into distinct parts

Kathrin Bringmann; Byungchan Kim; Eunmi Kim

doi:10.1007/s40687-025-00536-4

Modularity of 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 determine modularity properties of the generating function of sk(n) which sums k-th power of reciprocals of parts throughout all of the partitions of n into distinct parts. In particular, we show that the generating function for sk(n) is related to Maass Eisenstein series and sesquiharmonic Maass forms.

Original language	English
Article number	55
Journal	Research in Mathematical Sciences
Volume	12
Issue number	3
DOIs	https://doi.org/10.1007/s40687-025-00536-4
State	Published - Sep 2025

Keywords

Eichler integrals
Eisenstein Series
Integer partitions
Maass forms
Raising operator
Sesquiharmonic Maass forms
Sums of reciprocal parts

Access to Document

10.1007/s40687-025-00536-4

Cite this

@article{883e43106adf4efab3f21aa3ec47bd45,

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

abstract = "In this paper, we determine modularity properties of the generating function of sk(n) which sums k-th power of reciprocals of parts throughout all of the partitions of n into distinct parts. In particular, we show that the generating function for sk(n) is related to Maass Eisenstein series and sesquiharmonic Maass forms.",

keywords = "Eichler integrals, Eisenstein Series, Integer partitions, Maass forms, Raising operator, Sesquiharmonic Maass forms, Sums of reciprocal parts",

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

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.",

year = "2025",

month = sep,

doi = "10.1007/s40687-025-00536-4",

language = "English",

volume = "12",

journal = "Research in Mathematical Sciences",

issn = "2522-0144",

number = "3",

}

TY - JOUR

T1 - Modularity of moments of reciprocal sums for partitions into distinct parts

AU - Bringmann, Kathrin

AU - Kim, Byungchan

AU - Kim, Eunmi

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

PY - 2025/9

Y1 - 2025/9

N2 - In this paper, we determine modularity properties of the generating function of sk(n) which sums k-th power of reciprocals of parts throughout all of the partitions of n into distinct parts. In particular, we show that the generating function for sk(n) is related to Maass Eisenstein series and sesquiharmonic Maass forms.

AB - In this paper, we determine modularity properties of the generating function of sk(n) which sums k-th power of reciprocals of parts throughout all of the partitions of n into distinct parts. In particular, we show that the generating function for sk(n) is related to Maass Eisenstein series and sesquiharmonic Maass forms.

KW - Eichler integrals

KW - Eisenstein Series

KW - Integer partitions

KW - Maass forms

KW - Raising operator

KW - Sesquiharmonic Maass forms

KW - Sums of reciprocal parts

UR - https://www.scopus.com/pages/publications/105012758316

U2 - 10.1007/s40687-025-00536-4

DO - 10.1007/s40687-025-00536-4

M3 - Article

AN - SCOPUS:105012758316

SN - 2522-0144

VL - 12

JO - Research in Mathematical Sciences

JF - Research in Mathematical Sciences

IS - 3

M1 - 55

ER -

Modularity of moments of reciprocal sums for partitions into distinct parts

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this