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http://dx.doi.org/10.14317/jami.2022.813

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)
Publication Information
Journal of applied mathematics & informatics / v.40, no.5_6, 2022 , pp. 813-830 More about this Journal
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
Convolution sums; divisor function; quasimodular form;
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Times Cited By KSCI : 1  (Citation Analysis)
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