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

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 -