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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title = "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",

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.",

keywords = "Convolution sums, divisor function, quasimodular form",

author = "Park, \{Yoon Kyung\}",

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year = "2022",

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AU - Park, Yoon Kyung

PY - 2022

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N2 - 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.

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.

KW - Convolution sums

KW - divisor function

KW - quasimodular form

UR - https://www.scopus.com/pages/publications/85139109867

U2 - 10.14317/jami.2022.813

DO - 10.14317/jami.2022.813

M3 - Article

AN - SCOPUS:85139109867

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VL - 40

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JO - Journal of Applied Mathematics and Informatics

JF - Journal of Applied Mathematics and Informatics

IS - 5-6

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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