Non-vanishing of class group L-functions for number fields with a small regulator

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Abstract

Let be a number field of degree. We show that if then the fraction of class group characters for which the Hecke-function does not vanish at the central point is. The proof is an interplay between almost equidistribution of Eisenstein periods over the toral packet in associated to the maximal order of, and the escape of mass of the torus orbit associated to the trivial ideal class.

Original languageEnglish (US)
Pages (from-to)2423-2436
Number of pages14
JournalCompositio Mathematica
DOIs
StateAccepted/In press - 2020

Keywords

  • L-function
  • class group
  • equidistribution
  • escape of mass
  • non-vanishing
  • periodic torus orbit

ASJC Scopus subject areas

  • Algebra and Number Theory

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