Details
| Original language | English |
|---|---|
| Pages (from-to) | 1-42 |
| Number of pages | 42 |
| Journal | Revista matemática iberoamericana |
| Volume | 40 |
| Issue number | 1 |
| Early online date | 15 Dec 2023 |
| Publication status | Published - 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.
Keywords
- L-functions, Northcott property, abelian varieties, heights, motives
ASJC Scopus subject areas
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In: Revista matemática iberoamericana, Vol. 40, No. 1, 08.02.2024, p. 1-42.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the Northcott property for special values of L-functions
AU - Pazuki, Fabien
AU - Pengo, Riccardo
N1 - Funding Information: We would want to thank François Brunault, Jerson Caro, Marco d’Addezio, Richard Griffon, Roberto Gualdi, Marc Hindry, Matilde Lalín, Asbjørn Christian Nordentoft and Martin Widmer for useful discussions. We also thank the anonymous referees for their helpful comments and suggestions. The first author is supported by ANR-17-CE40-0012 Flair and ANR-20-CE40-0003 Jinvariant. The second author performed this work within the framework of the LABEX MILYON (ANR-10-LABX-0070) of the Université de Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). He is also thankful to the Max Planck Institute for Mathematics in Bonn for its hospitality and financial support. Both authors thank the IRN GANDA for its support. Riccardo Pengo received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 945714).
PY - 2024/2/8
Y1 - 2024/2/8
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 - L-functions
KW - Northcott property
KW - abelian varieties
KW - heights
KW - motives
UR - http://www.scopus.com/inward/record.url?scp=85187155210&partnerID=8YFLogxK
U2 - 10.4171/rmi/1454
DO - 10.4171/rmi/1454
M3 - Article
VL - 40
SP - 1
EP - 42
JO - Revista matemática iberoamericana
JF - Revista matemática iberoamericana
SN - 0213-2230
IS - 1
ER -