On the ring of arithmetic functions and the group of rational functions

In this thesis, firstly focused on arithmetic functions, dirichlet multiplication of arithmetic functions, basic definitions, theorems and the results related to multiplicative and complete multiplicative functions. Then the group of rational functions which were defined as a subgroup of multiplicative functions produced by complete multiplicative functions, generator functions and local properties of the group of rational functions were studied. According to these studies, a different method for obtaining Fibonacci and Lucas polynomials was examined. Finally the number sequences existing in the literature are obtained by using this method.