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

Ilya Khayutin

doi:10.1112/S0010437X20007472

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

Ilya Khayutin

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 language	English (US)
Pages (from-to)	2423-2436
Number of pages	14
Journal	Compositio Mathematica
DOIs	https://doi.org/10.1112/S0010437X20007472
State	Accepted/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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10.1112/S0010437X20007472

Cite this

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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.",

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AB - 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.

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KW - class group

KW - equidistribution

KW - escape of mass

KW - non-vanishing

KW - periodic torus orbit

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

Abstract

Keywords

ASJC Scopus subject areas

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