On the Northcott property for special values of L-functions
- Autores: Fabien Pazuki, Riccardo Pengo
- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 1, 2024, págs. 1-42
- Idioma: inglés
- DOI: 10.4171/RMI/1454
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Resumen
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.
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