# Evaluation of the convolution sums ∑ al + bm = n lσ(l)σ(m) withab≤ 9

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 1389-1399
- ISSN: 2391-5455

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topYoon Kyung Park. "Evaluation of the convolution sums ∑ al + bm = n lσ(l)σ(m) withab≤ 9." Open Mathematics 15.1 (2017): 1389-1399. <http://eudml.org/doc/288526>.

@article{YoonKyungPark2017,

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) \[\begin\{array\}\{\} \displaystyle \sum \limits \_\{al+bm=n\}\,l\sigma (l)\sigma (m) \end\{array\} \]
for all positive integers a, b and n with ab ≤ 9 and gcd(a, b) = 1.},

author = {Yoon Kyung Park},

journal = {Open Mathematics},

keywords = {Divisor function; Convolution sum; Quasimodular form},

language = {eng},

number = {1},

pages = {1389-1399},

title = {Evaluation of the convolution sums ∑ al + bm = n lσ(l)σ(m) withab≤ 9},

url = {http://eudml.org/doc/288526},

volume = {15},

year = {2017},

}

TY - JOUR

AU - Yoon Kyung Park

TI - Evaluation of the convolution sums ∑ al + bm = n lσ(l)σ(m) withab≤ 9

JO - Open Mathematics

PY - 2017

VL - 15

IS - 1

SP - 1389

EP - 1399

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 sums ∑al+bm=nlσ(l)σ(m) \[\begin{array}{} \displaystyle \sum \limits _{al+bm=n}\,l\sigma (l)\sigma (m) \end{array} \]
for all positive integers a, b and n with ab ≤ 9 and gcd(a, b) = 1.

LA - eng

KW - Divisor function; Convolution sum; Quasimodular form

UR - http://eudml.org/doc/288526

ER -

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