Eisenstein Series and Partition Functions

Sofiane Abdelhamid Atmani; Abdelmejid Bayad; Daeyeoul Kim

doi:10.1002/mma.11107

Eisenstein Series and Partition Functions

Sofiane Abdelhamid Atmani
, Abdelmejid Bayad
, Daeyeoul Kim^*

^*Corresponding author for this work

Department of Mathematics

University of Science and Technology Houari Boumediene
Université Paris-Saclay

Research output: Contribution to journal › Journal article › peer-review

Abstract

In this work, using quotients of Dedekind eta functions of weight (Formula presented.), we express certain Eisenstein series associated with congruence subgroups (Formula presented.), of arbitrary weight. We then obtain new Ramanujan type identities on partition functions associated with certain eta quotients. The method we apply in this work is inspired by the work of Fine, Kolberg, and Garvan on Eisenstein series. It is different from those used by Ramanujan, Zuckerman, Carlitz, and others.

Original language	English
Pages (from-to)	13355-13367
Number of pages	13
Journal	Mathematical Methods in the Applied Sciences
Volume	48
Issue number	14
DOIs	https://doi.org/10.1002/mma.11107
State	Published - 2025.09.30

Keywords

divisors functions
Eisenstein series
eta function
eta quotients
Hauptmodul
Legendre symbols
modular functions
partition functions
∖special t4ht@.<spispace>L-function

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1002/mma.11107

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title = "Eisenstein Series and Partition Functions",

abstract = "In this work, using quotients of Dedekind eta functions of weight (Formula presented.), we express certain Eisenstein series associated with congruence subgroups (Formula presented.), of arbitrary weight. We then obtain new Ramanujan type identities on partition functions associated with certain eta quotients. The method we apply in this work is inspired by the work of Fine, Kolberg, and Garvan on Eisenstein series. It is different from those used by Ramanujan, Zuckerman, Carlitz, and others.",

keywords = "divisors functions, Eisenstein series, eta function, eta quotients, Hauptmodul, Legendre symbols, modular functions, partition functions, ∖special t4ht@.<spispace>L-function",

author = "\{Abdelhamid Atmani\}, Sofiane and Abdelmejid Bayad and Daeyeoul Kim",

note = "Publisher Copyright: {\textcopyright} 2025 John Wiley \& Sons Ltd.",

year = "2025",

month = sep,

day = "30",

doi = "10.1002/mma.11107",

language = "English",

volume = "48",

pages = "13355--13367",

journal = "Mathematical Methods in the Applied Sciences",

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TY - JOUR

T1 - Eisenstein Series and Partition Functions

AU - Abdelhamid Atmani, Sofiane

AU - Bayad, Abdelmejid

AU - Kim, Daeyeoul

PY - 2025/9/30

Y1 - 2025/9/30

N2 - In this work, using quotients of Dedekind eta functions of weight (Formula presented.), we express certain Eisenstein series associated with congruence subgroups (Formula presented.), of arbitrary weight. We then obtain new Ramanujan type identities on partition functions associated with certain eta quotients. The method we apply in this work is inspired by the work of Fine, Kolberg, and Garvan on Eisenstein series. It is different from those used by Ramanujan, Zuckerman, Carlitz, and others.

AB - In this work, using quotients of Dedekind eta functions of weight (Formula presented.), we express certain Eisenstein series associated with congruence subgroups (Formula presented.), of arbitrary weight. We then obtain new Ramanujan type identities on partition functions associated with certain eta quotients. The method we apply in this work is inspired by the work of Fine, Kolberg, and Garvan on Eisenstein series. It is different from those used by Ramanujan, Zuckerman, Carlitz, and others.

KW - divisors functions

KW - Eisenstein series

KW - eta function

KW - eta quotients

KW - Hauptmodul

KW - Legendre symbols

KW - modular functions

KW - partition functions

KW - ∖special t4ht@.<spispace>L-function

UR - https://www.scopus.com/pages/publications/105007071563

U2 - 10.1002/mma.11107

DO - 10.1002/mma.11107

M3 - Journal article

AN - SCOPUS:105007071563

SN - 0170-4214

VL - 48

SP - 13355

EP - 13367

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 14

ER -

Eisenstein Series and Partition Functions

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

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