# 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

top

## Abstract

top
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) $\begin{array}{c}\sum _{al+bm=n}\phantom{\rule{0.166667em}{0ex}}l\sigma \left(l\right)\sigma \left(m\right)\end{array}$ for all positive integers a, b and n with ab ≤ 9 and gcd(a, b) = 1.

## How to cite

top

Yoon 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 -

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.