On the Northcott property for special values of \(L\)-functions

DOI10.4171/RMI/1454arXiv2012.00542OpenAlexW3107400440MaRDI QIDQ6199679

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Publication date: 28 February 2024

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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.

Full work available at URL: https://arxiv.org/abs/2012.00542

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