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.
Original language | English |
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Journal | Revista Matematica Iberoamericana |
Volume | 40 |
Issue number | 1 |
Pages (from-to) | 1-42 |
ISSN | 0213-2230 |
DOIs | |
Publication status | Published - 2024 |
Bibliographical note
Publisher Copyright:© 2023 Real Sociedad Matemática Española.
Keywords
- abelian varieties
- heights
- L-functions
- motives
- Northcott property