On the Northcott property for special values of L-functions

authored by

Fabien Pazuki, Riccardo Pengo

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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

University of Copenhagen

Type

Article

Journal

Revista matemática iberoamericana

Volume

40

Pages

1-42

No. of pages

42

ISSN

0213-2230

Publication date

08.02.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Mathematics(all)

Electronic version(s)

https://doi.org/10.4171/rmi/1454 (Access: Open)