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Toroidal families and averages of L-functions, I

Volume 214 / 2024

Étienne Fouvry, Emmanuel Kowalski, Philippe Michel Acta Arithmetica 214 (2024), 109-142 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.

Authors

  • Étienne FouvryUniversité Paris-Saclay, CNRS
    Laboratoire de Mathématiques d’Orsay
    91405 Orsay, France
    e-mail
  • Emmanuel KowalskiETH Zürich – D-MATH
    CH-8092 Zürich, Switzerland
    e-mail
  • Philippe MichelEPFL/SB/TAN, Station 8
    CH-1015 Lausanne, Switzerland
    e-mail

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