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 $L(\demi,χ^a)L(\demi,χ^b)$ for arbitrary integers~$a$ and~$b$ when $\chi$ varies over Dirichlet characters to a prime modulus.

29 pages; v3 (final version, to appear in Acta Arithmetica in volume dedicated to Henryk Iwaniec)