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- Title
On the Northcott property for special values of L-functions.
- Authors
Pazuki, Fabien; Pengo, Riccardo
- 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.
- Subjects
VALUATION of real property; L-functions; ZETA functions; ABELIAN varieties; DEDEKIND sums; RIEMANN hypothesis
- Publication
Revista Mathematica Iberoamericana, 2024, Vol 40, Issue 1, p1
- ISSN
0213-2230
- Publication type
Article
- DOI
10.4171/RMI/1454