Evaluation of the convolution sums al+bm=n lσ(l) σ(m) with ab ≤ 9

Yoon Kyung Park

doi:10.1515/math-2017-0116

Evaluation of the convolution sums _al+bm=n lσ(l) σ(m) with ab ≤ 9

Yoon Kyung Park

School of Natural Sciences

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

1 Scopus citations

Abstract

The generating functions of divisor functions are quasimodular forms of weight 2 and their products belong to a space of quasimodular forms of higher weight. In this article, we evaluate the convolution sums_al+bm=nlσ(l)σ(m) sum_al+bm=n σ(l)σ(m) for all positive integers a, b and n with ab ≤ 9 and gcd(a, b) = 1.

Original language	English
Pages (from-to)	1389-1399
Number of pages	11
Journal	Open Mathematics
Volume	15
Issue number	1
DOIs	https://doi.org/10.1515/math-2017-0116
State	Published - 2017

Keywords

Convolution sum
Divisor function
Quasimodular form

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abstract = "The generating functions of divisor functions are quasimodular forms of weight 2 and their products belong to a space of quasimodular forms of higher weight. In this article, we evaluate the convolution sumsal+bm=nlσ(l)σ(m) sumal+bm=n σ(l)σ(m) for all positive integers a, b and n with ab ≤ 9 and gcd(a, b) = 1.",

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AB - The generating functions of divisor functions are quasimodular forms of weight 2 and their products belong to a space of quasimodular forms of higher weight. In this article, we evaluate the convolution sumsal+bm=nlσ(l)σ(m) sumal+bm=n σ(l)σ(m) for all positive integers a, b and n with ab ≤ 9 and gcd(a, b) = 1.

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KW - Divisor function

KW - Quasimodular form

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Evaluation of the convolution sums _al+bm=n lσ(l) σ(m) with ab ≤ 9

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Keywords

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