On the Northcott property for special values of L-functions
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On the Northcott property for special values of L-functions. / Pazuki, Fabien; Pengo, Riccardo.
I: Revista Matematica Iberoamericana, Bind 40, Nr. 1, 2024, s. 1-42.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - On the Northcott property for special values of L-functions
AU - Pazuki, Fabien
AU - Pengo, Riccardo
N1 - Publisher Copyright: © 2023 Real Sociedad Matemática Española.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
KW - abelian varieties
KW - heights
KW - L-functions
KW - motives
KW - Northcott property
U2 - 10.4171/rmi/1454
DO - 10.4171/rmi/1454
M3 - Journal article
AN - SCOPUS:85187155210
VL - 40
SP - 1
EP - 42
JO - Revista Matematica Iberoamericana
JF - Revista Matematica Iberoamericana
SN - 0213-2230
IS - 1
ER -
ID: 385895322