Identities for a Special Finite Sum Related to the Dedekind Sums and Fibonacci Numbers

Authors : Elif ÇETİN

Pages : 232-240

Doi:10.54287/gujsa.1280707

View : 39 | Download : 33

Publication Date : 2023-06-27

Article Type : Research Paper

Abstract :The origin of this article is to achieve original equations related to the special finite sum Cinsert ignore into journalissuearticles values(μ,β;1);, which is connected with Dedekind, Hardy, Simsek, and many other finite sums. By using the analytic properties of this sum, many useful identities are established between the Cinsert ignore into journalissuearticles values(μ,β;1); sum and other well-known finite sums. Through the use of these identities, the reciprocity law of this sum is obtained. Furthermore, another reciprocity law of the sum Cinsert ignore into journalissuearticles values(μ,β;1); is presented for μ and β are particular Fibonacci numbers. This remarkable result establishes a connection between number theory and analysis.
Keywords : Hardy Sums, Dedekind Sums, Simsek Sums, Fibonacci Numbers