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arXiv · 2012.00542

On the Northcott property for special values of L-functions

Fabien Pazuki·Riccardo Pengo
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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.

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Fabien Pazuki, Riccardo Pengo. 2020-12-01. On the Northcott property for special values of L-functions. https://doi.org/10.4171/rmi%2F1454

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