Applications of Liouville’s Identity with an Odd Function
Aeran Kim *
Department of Mathematics, Chonbuk National University, South Korea.
Keum Yeon Lee
Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University, South Korea.
Hwasin Park
Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University, South Korea.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we are based on the Huard, Ou, Spearman and Williams’s generalization of Liouville’s
Identity so we obtain
and etc. Also, independently we attempt to consider the Liouville’s Identity, therefore as the application of his identity, we have the restricted combinatoric convolution sums as
(see Theorem 1.6 and Theorem 1.8) and etc., by dealing with an odd function for m, n ∈ 
and l ∈ ∪ {0}.
Keywords: Divisor functions, Convolution sums.