On the Northcott property for special values of L-functions

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On the Northcott property for special values of L-functions. / Pazuki, Fabien; Pengo, Riccardo.

I: Revista Matematica Iberoamericana, Bind 40, Nr. 1, 2024, s. 1-42.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Pazuki, F & Pengo, R 2024, 'On the Northcott property for special values of L-functions', Revista Matematica Iberoamericana, bind 40, nr. 1, s. 1-42. https://doi.org/10.4171/rmi/1454

APA

Pazuki, F., & Pengo, R. (2024). On the Northcott property for special values of L-functions. Revista Matematica Iberoamericana, 40(1), 1-42. https://doi.org/10.4171/rmi/1454

Vancouver

Pazuki F, Pengo R. On the Northcott property for special values of L-functions. Revista Matematica Iberoamericana. 2024;40(1):1-42. https://doi.org/10.4171/rmi/1454

Author

Pazuki, Fabien ; Pengo, Riccardo. / On the Northcott property for special values of L-functions. I: Revista Matematica Iberoamericana. 2024 ; Bind 40, Nr. 1. s. 1-42.

Bibtex

@article{649b826d249f4117b9466f5e22e0ecc9,
title = "On the Northcott property for special values of L-functions",
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.",
keywords = "abelian varieties, heights, L-functions, motives, Northcott property",
author = "Fabien Pazuki and Riccardo Pengo",
note = "Publisher Copyright: {\textcopyright} 2023 Real Sociedad Matem{\'a}tica Espa{\~n}ola.",
year = "2024",
doi = "10.4171/rmi/1454",
language = "English",
volume = "40",
pages = "1--42",
journal = "Revista Matematica Iberoamericana",
issn = "0213-2230",
publisher = "Universidad Autonoma de Madrid",
number = "1",

}

RIS

TY - JOUR

T1 - On the Northcott property for special values of L-functions

AU - Pazuki, Fabien

AU - Pengo, Riccardo

N1 - Publisher Copyright: © 2023 Real Sociedad Matemática Española.

PY - 2024

Y1 - 2024

N2 - 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.

AB - 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.

KW - abelian varieties

KW - heights

KW - L-functions

KW - motives

KW - Northcott property

U2 - 10.4171/rmi/1454

DO - 10.4171/rmi/1454

M3 - Journal article

AN - SCOPUS:85187155210

VL - 40

SP - 1

EP - 42

JO - Revista Matematica Iberoamericana

JF - Revista Matematica Iberoamericana

SN - 0213-2230

IS - 1

ER -

ID: 385895322