Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2012.12.10
  • Published : 2013.07.31
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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.

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References

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