Evaluation of the convolution sums ∑ak+bl+cm=nσ(k)σ(l)σ(m) with lcm(a,b,c) = 7,8 or 9-Reference-Cited by-同舟云学术

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

Published:2018-07 Issue:06 Volume:14 Page:1637-1650
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Park Yoon Kyung¹

Affiliation:

1. Department of Mathematics Education, Gongju National University of Education 27, Ungjin-ro, Gongju-si, Chungcheongnam-do, 32553, South Korea

Abstract

It is known that the generating functions of divisor functions are quasimodular forms of weight [Formula: see text]. Hence their product is a quasimodular form of higher weight. In this paper, we evaluate the convolution sums [Formula: see text] for all positive integers [Formula: see text] with [Formula: see text] or [Formula: see text] using theory of modular form.

Funder

National Research Foundation of Korea

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042118500999

Reference25 articles.

1. Evaluation of the convolution sums \sum_{l+18m=n} \sigma(l) \sigma(m) and \sum_{2l+9m=n} \sigma(l) \sigma(m)

2. The Convolution Sum Σm

3. Evaluation of the convolution sums ∑l+27m=nσ(l)σ(m) and ∑l+32m=nσ(l)σ(m)

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