Bertrand’s and Rodriguez Villegas’ conjecture for real multi-quadratic Galois extensions of the rationals
Abstract
The conjecture due to Bertrand and Rodriguez Villegas asserts that the 1-norm of the nonzero element in an exterior power of the units of a number field has a certain lower bound. We prove this conjecture for the exterior square case when the number field is a real multi-quadratic Galois extension of any degree of the rationals.
Fields of Study & Subjects
Polynomial and algebraic computation
Algebraic Geometry and Number Theory
Commutative Algebra and Its Applications
Publication details
- Journal / source
- Journal de Théorie des Nombres de Bordeaux
- Volume
- 38
- Issue
- 1
- Pages
- 57–69
- Publication date
- 24 April 2026
- Language
- EN