On the Northcott property for special values of L-functions
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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.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Revista Matematica Iberoamericana |
| Vol/bind | 40 |
| Udgave nummer | 1 |
| Sider (fra-til) | 1-42 |
| ISSN | 0213-2230 |
| DOI | |
| Status | Udgivet - 2024 |
Bibliografisk note
Funding Information:
Funding. 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).
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).
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