TY - JOUR
T1 - Evaluation of the convolution sums ∑ ak+bl+cm = n σ (k) σ (l) σ (m) with lcm (a, b, c) = 7, 8 or 9
AU - Park, Yoon Kyung
N1 - Publisher Copyright:
© 2018 World Scientific Publishing Company.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - It is known that the generating functions of divisor functions are quasimodular forms of weight 2. Hence their product is a quasimodular form of higher weight. In this paper, we evaluate the convolution sums ak+bl+cm=nσ(k)σ(l)σ(m) for all positive integers a,b,c,n with lcm(a,b,c) = 7, 8 or 9 using theory of modular form.
AB - It is known that the generating functions of divisor functions are quasimodular forms of weight 2. Hence their product is a quasimodular form of higher weight. In this paper, we evaluate the convolution sums ak+bl+cm=nσ(k)σ(l)σ(m) for all positive integers a,b,c,n with lcm(a,b,c) = 7, 8 or 9 using theory of modular form.
KW - convolution sum
KW - Divisor functions
KW - quasimodular form
UR - http://www.scopus.com/inward/record.url?scp=85040660871&partnerID=8YFLogxK
U2 - 10.1142/S1793042118500999
DO - 10.1142/S1793042118500999
M3 - Article
AN - SCOPUS:85040660871
SN - 1793-0421
VL - 14
SP - 1637
EP - 1650
JO - International Journal of Number Theory
JF - International Journal of Number Theory
IS - 6
ER -