I am sorry for being rude in my previous thread, I would like to apologize and resubmit my question with all the correct notation and hopefully present it more clearer. My text is Elementary Number Theory by Jones and Jones. I do not understand Dirichlet product and series well at all. I am sure the definitions and lemmas in my text would be enough to tackle these problems, but I cannot seem to grasp them. Any help would be greatly appreciated, and I thank you for your time.
is a positive integer and and are arithmetic functions. denotes the Dirichlet series for , so
Suppose is completely multiplicative. Define inductively by = and = .
(f) If is non-zero, then