On the Northcott property for special values of L-functions

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • Fabien Pazuki
  • Riccardo Pengo

Externe Organisationen

  • Københavns Universitet
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)1-42
Seitenumfang42
FachzeitschriftRevista matemática iberoamericana
Jahrgang40
Ausgabenummer1
Frühes Online-Datum15 Dez. 2023
PublikationsstatusVeröffentlicht - 8 Feb. 2024

Abstract

We propose an investigation on the Northcott, Bogomolov and Lehmer properties for special values of L-functions. We first introduce an axiomatic approach to these three properties. We then focus on the Northcott property for special values of L-functions. In the case of L-functions of pure motives, we prove a Northcott property for special values located at the left of the critical strip, assuming that the L-functions in question satisfy some expected properties. Inside the critical strip, focusing on the Dedekind zeta function of number fields, we prove that such a property does not hold for the special value at one, but holds for the special value at zero, and we give a related quantitative estimate in this case.

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On the Northcott property for special values of L-functions. / Pazuki, Fabien; Pengo, Riccardo.
in: Revista matemática iberoamericana, Jahrgang 40, Nr. 1, 08.02.2024, S. 1-42.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Pazuki F, Pengo R. On the Northcott property for special values of L-functions. Revista matemática iberoamericana. 2024 Feb 8;40(1):1-42. Epub 2023 Dez 15. doi: 10.4171/rmi/1454
Pazuki, Fabien ; Pengo, Riccardo. / On the Northcott property for special values of L-functions. in: Revista matemática iberoamericana. 2024 ; Jahrgang 40, Nr. 1. S. 1-42.
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abstract = "We propose an investigation on the Northcott, Bogomolov and Lehmer properties for special values of L-functions. We first introduce an axiomatic approach to these three properties. We then focus on the Northcott property for special values of L-functions. In the case of L-functions of pure motives, we prove a Northcott property for special values located at the left of the critical strip, assuming that the L-functions in question satisfy some expected properties. Inside the critical strip, focusing on the Dedekind zeta function of number fields, we prove that such a property does not hold for the special value at one, but holds for the special value at zero, and we give a related quantitative estimate in this case.",
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