EVALUATION OF THE CONVOLUTION SUMS ∑ ak+bl+cm=nσ(k)σ(l)σ(m),∑al+bm=nlσ(l)σ(m)AND∑al+bm=nσ3(l)σ(m) FOR DIVISORS a, b, c OF 10

Yoon Kyung Park

doi:10.14317/jami.2022.813

EVALUATION OF THE CONVOLUTION SUMS ∑ ak+bl+cm=n^{σ(k)σ(l)σ(m),∑}al+bm=n^{lσ(l)σ(m)AND∑}al+bm=n^σ3(l)σ(m) FOR DIVISORS a, b, c OF 10

Yoon Kyung Park

School of Natural Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

The generating functions of the divisor function (formula presented) 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(formula presented) with lcm(a, b, c) = 10 and (formula presented) and (formula presented) with lcm(a, b) = 10.

Original language	English
Pages (from-to)	813-830
Number of pages	18
Journal	Journal of Applied Mathematics and Informatics
Volume	40
Issue number	5-6
DOIs	https://doi.org/10.14317/jami.2022.813
State	Published - 2022

Keywords

Convolution sums
divisor function
quasimodular form

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10.14317/jami.2022.813

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abstract = "The generating functions of the divisor function (formula presented) 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(formula presented) with lcm(a, b, c) = 10 and (formula presented) and (formula presented) with lcm(a, b) = 10.",

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AB - The generating functions of the divisor function (formula presented) 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(formula presented) with lcm(a, b, c) = 10 and (formula presented) and (formula presented) with lcm(a, b) = 10.

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KW - divisor function

KW - quasimodular form

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ER -

EVALUATION OF THE CONVOLUTION SUMS ∑ ak+bl+cm=n^{σ(k)σ(l)σ(m),∑}al+bm=n^{lσ(l)σ(m)AND∑}al+bm=n^σ3(l)σ(m) FOR DIVISORS a, b, c OF 10

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