[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2013.50.4.1389

CONVOLUTION SUMS AND THEIR RELATIONS TO EISENSTEIN SERIES

Kim, Daeyeoul (National Institute for Mathematical Sciences)
Kim, Aeran (Department of Mathematics and Institute of Pure and Applied Mathematics Chonbuk National University)
Sankaranarayanan, Ayyadurai (School of Mathematics Tata Institute of Fundamental Research)

Publication Information

Bulletin of the Korean Mathematical Society / v.50, no.4, 2013 , pp. 1389-1413 More about this Journal

Abstract

In this paper, we consider several convolution sums, namely, $\mathcal{A}_i(m,n;N)$ ( $i=1,2,3,4$ ), $\mathcal{B}_j(m,n;N)$ ( $j=1,2,3$ ), and $\mathcal{C}_k(m,n;N)$ ( $k=1,2,3,{\cdots},12$ ), 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 involving the Weierstrass ${\wp}$ -function, its derivative and certain linear combination of Eisenstein series is established.

Keywords

sum of divisor functions; convolution sums; Faulhaber sums; Eisenstein series; elliptic function;

Citations & Related Records

Times Cited By KSCI : 3 (Citation Analysis)

Reference
Cited By KSCI

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