On the Northcott property for special values of L-functions

Fabien Pazuki, Riccardo Pengo

Published 2020-12-01Version 1

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. We prove that such a property holds for the special value at zero of Dedekind zeta functions of number fields. 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 the validity of the functional equation.