Relative Bogomolov extensions

Grizzard, Robert

doi:10.4064/aa170-1-1

Cited by 6 publications

(5 citation statements)

References 15 publications

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“…First of all, it is known that h has the Northcott or Bogomolov property, when restricted to suitable sub-fields of Q having infinite degree over Q. We refer the interested reader to [16,29,30,46,51,139] for the study of fields having the Northcott property, and to [3,4,16,53,54,56,64,72,115,119] for the study of fields having the Bogomolov one. Moreover, it has also been shown that many fields F Â Q do not have the Bogomolov property.…”

Section: Logarithmic Weil Heightmentioning

confidence: 99%

On the Northcott property for special values of L-functions

Pazuki,

Pengo

2024

Rev. Mat. Iberoam.

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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.

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Section: Logarithmic Weil Heightmentioning

confidence: 99%

On the Northcott property for special values of L-functions

Pazuki,

Pengo

2024

Rev. Mat. Iberoam.

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“…First of all, it is known that h has the Northcott or Bogomolov property, when restricted to suitable sub-fields of Q having infinite degree over Q. We refer the interested reader to [12,26,98,20,29,18] for the study of fields having the Northcott property, and to [12,4,50,87,3,43,36,33,32,84] for the study of fields having the Bogomolov one. Moreover, it has also been shown that many fields F ⊆ Q do not have the Bogomolov property.…”

Section: 2mentioning

confidence: 99%

On the Northcott property for special values of L-functions

Pazuki¹,

Pengo²

2020

Preprint

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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.

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“…. So 0-Northcott and 0-Bogomolov are the usual Northcott and Bogomolov property (formally introduced by Bombieri and Zannier [4], and studied, e.g., in [4,6,2,3,1,9,5,7,11,8]), whereas 1-Bogomolov was recently introduced by Pazuki and Pengo in [10] as Lehmer property. The authors of the latter article implicitly raised the problem of constructing a field with Lehmer property that fails to have Bogomolov property.…”

Section: Introductionmentioning

confidence: 99%