Toroidal families and averages of L-functions, I
Acta Arithmetica
MSC: Primary 11M06; Secondary 11T23, 11A07
DOI: 10.4064/aa230323-24-5
Published online: 17 June 2024
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 ${\rm L}\big (\frac 12,\chi ^a\big ){\rm L}\big (\frac 12,\chi ^b\big )$ for arbitrary integers $a$ and $b$ when $\chi $ varies over Dirichlet characters of a given prime modulus.
