Evaluation of the convolution sums ∑ ak+bl+cm = n σ (k) σ (l) σ (m) with lcm (a, b, c) = 7, 8 or 9

Yoon Kyung Park

doi:10.1142/S1793042118500999

Evaluation of the convolution sums ∑ ak+bl+cm = n σ (k) σ (l) σ (m) with lcm (a, b, c) = 7, 8 or 9

Yoon Kyung Park

School of Natural Sciences

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

4 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1637-1650
Number of pages	14
Journal	International Journal of Number Theory
Volume	14
Issue number	6
DOIs	https://doi.org/10.1142/S1793042118500999
State	Published - 1 Jul 2018

Keywords

convolution sum
Divisor functions
quasimodular form

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10.1142/S1793042118500999

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abstract = "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.",

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KW - Divisor functions

KW - quasimodular form

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Evaluation of the convolution sums ∑ ak+bl+cm = n σ (k) σ (l) σ (m) with lcm (a, b, c) = 7, 8 or 9

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