Arithmetic properties derived from coefficients of certain eta quotients

Jihyun Hwang; Yan Li; Daeyeoul Kim

doi:10.1186/s13660-020-02368-y

Arithmetic properties derived from coefficients of certain eta quotients

Jihyun Hwang
, Yan Li
, Daeyeoul Kim^*

^*Corresponding author for this work

Department of Mathematics

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

3 Scopus citations

Abstract

For a positive integer k, let F(q)k:=∏n≥1(1−qn)4k(1+q2n)2k=∑n≥0ak(n)qn be the eta quotients. The coefficients a₁(n) can be interpreted as a certain kind of restricted divisor sums. In this paper, we give the signs and modulo values for a₁(n) and a₂(m) and calculate several convolution sums involving a_k(n).

Original language	English
Article number	104
Journal	Journal of Inequalities and Applications
Volume	2020
Issue number	1
DOIs	https://doi.org/10.1186/s13660-020-02368-y
State	Published - 2020

Keywords

Convolution sums
Eta quotient
q-series
Restricted divisor functions

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1186/s13660-020-02368-y

Cite this

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title = "Arithmetic properties derived from coefficients of certain eta quotients",

abstract = "For a positive integer k, let F(q)k:=∏n≥1(1−qn)4k(1+q2n)2k=∑n≥0ak(n)qn be the eta quotients. The coefficients a1(n) can be interpreted as a certain kind of restricted divisor sums. In this paper, we give the signs and modulo values for a1(n) and a2(m) and calculate several convolution sums involving ak(n).",

keywords = "Convolution sums, Eta quotient, q-series, Restricted divisor functions",

author = "Jihyun Hwang and Yan Li and Daeyeoul Kim",

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language = "English",

volume = "2020",

journal = "Journal of Inequalities and Applications",

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T1 - Arithmetic properties derived from coefficients of certain eta quotients

AU - Hwang, Jihyun

AU - Li, Yan

AU - Kim, Daeyeoul

PY - 2020

Y1 - 2020

N2 - For a positive integer k, let F(q)k:=∏n≥1(1−qn)4k(1+q2n)2k=∑n≥0ak(n)qn be the eta quotients. The coefficients a1(n) can be interpreted as a certain kind of restricted divisor sums. In this paper, we give the signs and modulo values for a1(n) and a2(m) and calculate several convolution sums involving ak(n).

AB - For a positive integer k, let F(q)k:=∏n≥1(1−qn)4k(1+q2n)2k=∑n≥0ak(n)qn be the eta quotients. The coefficients a1(n) can be interpreted as a certain kind of restricted divisor sums. In this paper, we give the signs and modulo values for a1(n) and a2(m) and calculate several convolution sums involving ak(n).

KW - Convolution sums

KW - Eta quotient

KW - q-series

KW - Restricted divisor functions

UR - https://www.scopus.com/pages/publications/85083525955

U2 - 10.1186/s13660-020-02368-y

DO - 10.1186/s13660-020-02368-y

M3 - Journal article

AN - SCOPUS:85083525955

SN - 1025-5834

VL - 2020

JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

IS - 1

M1 - 104

ER -

Arithmetic properties derived from coefficients of certain eta quotients

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

Access to Document

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