Toroidal families and averages of L-functions, I

Abstract

We initiate the study of certain families of L-functions attached to characters of subgroups of higher-rank tori, and of their average at the central point. In particular, we evaluate the average of the values L(1/2 , χᵃ)L(1/2 , χᵇ) for arbitrary integers a and b when χ varies over Dirichlet characters of a given prime modulus.