On the success and failure of Gram's Law and the Rosser Rule
We give a method of obtaining explicit formulas for various mean values of Dirichlet L-functions which are expressed in terms of the Riemann zeta-function, the Euler function and Jordan's totient functions. Applying those results to mean values of Dirichlet L-functions, we also give an explicit formula for certain mean values of double Dirichlet L-functions.
On étudie sommairement la distribution des valeurs de ( : caractère de Dirichlet primitif réel) et on constate qu’on a en général ; on démontre par ailleurs que si , alors ( : conducteur de ; : constante positive effectivement calculable.