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.