Generalizations of Dirichlet convolution
The thesis reviews Dirichlet convolution of arithmetic functions and some generalizations. First, we present the main properties of the Dirichlet convolution on the set of arithmetic functions and some characterizations of prime numbers via arithmetic functions are given. Then we explore the K-convolution and the regular convolutions and finally we extend the study of Dirichlet convolution in categories. We give also an example for the evaluation of the Mobius function of a Mobius category.
Villarreal, Juan Carlos, "Generalizations of Dirichlet convolution" (2013). ETD Collection for University of Texas, El Paso. AAI1540011.