I will seperate my next 2 questions into 2 separate threads so that it does not get cluttered. I don't know if the following definition is needed, but I will include it.

is a positive integer and and are arithmetic functions. denotes the Dirichlet series for , so

=

(1) Define = . Show that

(a) If then for all primes and all

=

(b) (s)=

Any help would be appreciated, thanks!