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.
In this report, prepared specially for the program of the XXVième Journées Arithmétiques, we describe how, in joint work with K. Soundararajan and Antal Balog, we have developed the notion of “pretentiousness” to help us better understand several key questions in analytic number theory.