Constructing totally p-adic numbers of small height - Archive ouverte HAL
Article Dans Une Revue International Journal of Number Theory Année : 2021

Constructing totally p-adic numbers of small height

Sara Checcoli
A. Fehm
  • Fonction : Auteur

Résumé

Bombieri and Zannier gave an effective construction of algebraic numbers of small height inside the maximal Galois extension of the rationals which is totally split at a given finite set of prime numbers. They proved, in particular, an explicit upper bound for the lim inf of the height of elements in such fields. We generalize their result in an effective way to maximal Galois extensions of number fields with given local behavior at finitely many places.

Dates et versions

hal-04706301 , version 1 (23-09-2024)

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Citer

Sara Checcoli, A. Fehm. Constructing totally p-adic numbers of small height. International Journal of Number Theory, 2021, 18 (03), pp.501-514. ⟨10.1142/S1793042122500294⟩. ⟨hal-04706301⟩
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