Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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EVALUATION OF THE CONVOLUTION SUMS Σak+bl+cm=n σ(k)σ(l)σ(m), Σal+bm=n lσ(l)σ(m) AND Σal+bm=n σ3(l)σ(m) FOR DIVISORS a, b, c OF 10

  • PARK, YOON KYUNG (School of Liberal Arts, Seoul National University of Science and Technology)
  • Received : 2022.03.18
  • Accepted : 2022.06.18
  • Published : 2022.09.30
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Abstract

The generating functions of the divisor function σs(n) = Σ0<d|n ds are quasimodular forms. In this paper, we find the basis of the space of quasimodular forms of weight 6 on Γ0(10) consisting of Eisenstein series and η-quotients. Then we evaluate the convolution sum Σak+bl+cm=n σ(k)σ(l)σ(m) with lcm(a, b, c) = 10 and Σal+bm=n lσ(l)σ(m) and Σal+bm=n σ3(l)σ(m) with lcm(a, b) = 10.

Keywords

Acknowledgement

This study was financially supported by NRF 2021R1F1A1055200.

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