REMARKS OF CONGRUENT ARITHMETIC SUMS OF THETA FUNCTIONS DERIVED FROM DIVISOR FUNCTIONS

• Journal title : Honam Mathematical Journal
• Volume 35, Issue 3,  2013, pp.351-372
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2013.35.3.351
Title & Authors
REMARKS OF CONGRUENT ARITHMETIC SUMS OF THETA FUNCTIONS DERIVED FROM DIVISOR FUNCTIONS
Kim, Aeran; Kim, Daeyeoul; Ikikardes, Nazli Yildiz;

Abstract
In this paper, we study a distinction the two generating functions : $\small{{\varphi}^k(q)=\sum_{n=0}^{\infty}r_k(n)q^n}$ and $\small{{\varphi}^{*,k}(q)={\varphi}^k(q)-{\varphi}^k(q^2)}$ ($\small{k}$ = 2, 4, 6, 8, 10, 12, 16), where $\small{r_k(n)}$ is the number of representations of $\small{n}$ as the sum of $\small{k}$ squares. We also obtain some congruences of representation numbers and divisor function.
Keywords
Infinite product;Convolution sums;Congruent sums;
Language
English
Cited by
1.
Bernoulli numbers and certain convolution sums with divisor functions, Advances in Difference Equations, 2013, 2013, 1, 277
2.
THE RELATION PROPERTY BETWEEN THE DIVISOR FUNCTION AND INFINITE PRODUCT SUMS, Honam Mathematical Journal, 2016, 38, 3, 507
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