CONVOLUTION SUMS AND THEIR RELATIONS TO EISENSTEIN SERIES

Title & Authors
CONVOLUTION SUMS AND THEIR RELATIONS TO EISENSTEIN SERIES
Kim, Daeyeoul; Kim, Aeran; Sankaranarayanan, Ayyadurai;

Abstract
In this paper, we consider several convolution sums, namely, $\small{\mathcal{A}_i(m,n;N)}$ ($\small{i=1,2,3,4}$), $\small{\mathcal{B}_j(m,n;N)}$ ($\small{j=1,2,3}$), and $\small{\mathcal{C}_k(m,n;N)}$ ($\small{k=1,2,3,{\cdots},12}$), 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 $\small{{\wp}}$-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;
Language
English
Cited by
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