Convolution sums and their relations to eisenstein series

Daeyeoul Kim; Aeran Kim; Ayyadurai Sankaranarayanan

doi:10.4134/BKMS.2013.50.4.1389

Convolution sums and their relations to eisenstein series

Daeyeoul Kim
, Aeran Kim
, Ayyadurai Sankaranarayanan

Department of Mathematics

National Institute for Mathematical Sciences
Jeonbuk National University
Tata Institute of Fundamental Research

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

1 Scopus citations

Abstract

In this paper, we consider several convolution sums, namely, A_i(m; n; N) (i = 1; 2; 3; 4), B_j (m; n;N) (j = 1; 2; 3), and C_k(m; n;N) (k = 1; 2; 3;:::, 12), and establish certain identities involving their finite products. Then we extend these types of product convolution identities to products involving Faulhaber sums. As an application, an identity in- volving the Weierstrass ℘-function, its derivative and certain linear com- bination of Eisenstein series is established.

Original language	English
Pages (from-to)	1389-1413
Number of pages	25
Journal	Bulletin of the Korean Mathematical Society
Volume	50
Issue number	4
DOIs	https://doi.org/10.4134/BKMS.2013.50.4.1389
State	Published - 2013

Keywords

Convolution sums
Eisenstein series
Elliptic function
Faulhaber sums
Sum of divisor functions

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.4134/BKMS.2013.50.4.1389

Cite this

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title = "Convolution sums and their relations to eisenstein series",

abstract = "In this paper, we consider several convolution sums, namely, Ai(m; n; N) (i = 1; 2; 3; 4), Bj (m; n;N) (j = 1; 2; 3), and Ck(m; n;N) (k = 1; 2; 3;:::, 12), and establish certain identities involving their finite products. Then we extend these types of product convolution identities to products involving Faulhaber sums. As an application, an identity in- volving the Weierstrass ℘-function, its derivative and certain linear com- bination of Eisenstein series is established.",

keywords = "Convolution sums, Eisenstein series, Elliptic function, Faulhaber sums, Sum of divisor functions",

author = "Daeyeoul Kim and Aeran Kim and Ayyadurai Sankaranarayanan",

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doi = "10.4134/BKMS.2013.50.4.1389",

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TY - JOUR

T1 - Convolution sums and their relations to eisenstein series

AU - Kim, Daeyeoul

AU - Kim, Aeran

AU - Sankaranarayanan, Ayyadurai

PY - 2013

Y1 - 2013

N2 - In this paper, we consider several convolution sums, namely, Ai(m; n; N) (i = 1; 2; 3; 4), Bj (m; n;N) (j = 1; 2; 3), and Ck(m; n;N) (k = 1; 2; 3;:::, 12), and establish certain identities involving their finite products. Then we extend these types of product convolution identities to products involving Faulhaber sums. As an application, an identity in- volving the Weierstrass ℘-function, its derivative and certain linear com- bination of Eisenstein series is established.

AB - In this paper, we consider several convolution sums, namely, Ai(m; n; N) (i = 1; 2; 3; 4), Bj (m; n;N) (j = 1; 2; 3), and Ck(m; n;N) (k = 1; 2; 3;:::, 12), and establish certain identities involving their finite products. Then we extend these types of product convolution identities to products involving Faulhaber sums. As an application, an identity in- volving the Weierstrass ℘-function, its derivative and certain linear com- bination of Eisenstein series is established.

KW - Convolution sums

KW - Eisenstein series

KW - Elliptic function

KW - Faulhaber sums

KW - Sum of divisor functions

UR - https://www.scopus.com/pages/publications/84887092314

U2 - 10.4134/BKMS.2013.50.4.1389

DO - 10.4134/BKMS.2013.50.4.1389

M3 - Journal article

AN - SCOPUS:84887092314

SN - 1015-8634

VL - 50

SP - 1389

EP - 1413

JO - Bulletin of the Korean Mathematical Society

JF - Bulletin of the Korean Mathematical Society

IS - 4

ER -

Convolution sums and their relations to eisenstein series

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

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