Evaluation of Certain Convolution Sums Involving Divisor Functions and Infinite Product Sums

2015 ◽  
Vol 5 (6) ◽  
pp. 666-704
Keyword(s):  
Infinite Product ◽  
Convolution Sums ◽  
Divisor Functions

scholarly journals A PRODUCT FORMULA FOR COMBINATORIC CONVOLUTION SUMS OF ODD DIVISOR FUNCTIONS

2016 ◽  
Vol 38 (2) ◽  
pp. 243-257
Author(s):  
Kwangchul Lee ◽  
Daeyeoul Kim ◽  
Gyeong-Sig Seo
Keyword(s):  
Product Formula ◽  
Convolution Sums ◽  
Divisor Functions

scholarly journals CONVOLUTION SUMS ARISING FROM DIVISOR FUNCTIONS

2013 ◽  
Vol 50 (2) ◽  
pp. 331-360 ◽  
Author(s):  
Aeran Kim ◽  
Daeyeoul Kim ◽  
Li Yan
Keyword(s):  
Convolution Sums ◽  
Divisor Functions

scholarly journals A study of approximate normal distribution derived from combinatoric convolution sums of divisor functions

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1811-1821
Author(s):  
Daeyeoul Kim ◽  
Kwangchul Lee ◽  
Gyeong-Sig Seo
Keyword(s):  
Normal Distribution ◽  
Legendre Polynomials ◽  
Bernoulli Polynomials ◽  
Convolution Sums ◽  
Divisor Functions

In this paper, we consider the relations between Bernoulli polynomials, Legendre polynomials and combinatoric convolution sums of divisor functions. In addition, we give examples of approximate normal distribution derived from combinatoric convolution sums of divisor functions.

scholarly journals The multinomial convolution sums of certain divisor functions

2017 ◽  
Vol 448 (2) ◽  
pp. 1163-1174 ◽  
Author(s):  
Bumkyu Cho ◽  
Daeyeoul Kim ◽  
Ho Park
Keyword(s):  
Convolution Sums ◽  
Divisor Functions

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

2018 ◽  
Vol 14 (06) ◽  
pp. 1637-1650 ◽  
Author(s):  
Yoon Kyung Park
Keyword(s):  
Modular Form ◽  
Generating Functions ◽  
Convolution Sums ◽  
Divisor Functions ◽  
Positive Integers

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.

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