Mean value theorems for a class of density like arithmetic function

In this talk we present mean value theorems for arithmetic functions F defined by a convolution product: F(n)=prod_{d|n} g(d); where g is an arithmetic function taking values in (0, 1] and satisfying some generic conditions. This is mainly motivated by the problem of studying densitites of primitive and normal elements over finite fields. In particular, we prove that the density M_q(n) (resp. P_q(n)) of normal (resp. primitive) elements in the finite field extension F_{q^n} of F_q are arithmetic functions of (non zero) mean values. We also provide further results on the behaviour of the function M_q(n).