On the Northcott property for special values of L-functions

Pazuki, Fabien; Pengo, Riccardo

doi:10.4171/rmi/1454

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On the Northcott property for special values of L-functions

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Pengo, Riccardo
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.48550/arXiv.2012.00542
(Preprint)

https://doi.org/10.4171/rmi/1454
(Publisher version)

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2012.00542.pdf
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Pazuki-Pengo_On the Northcott property for special values of L-functions_2024.pdf
(Publisher version), 727KB

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Citation

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

Cite as: https://hdl.handle.net/21.11116/0000-000E-2A9D-3

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.