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arXiv · 2410.03238

Bertrand's and Rodriguez Villegas' conjecture for real multi-quadratic Galois extensions of the rationals

Dohyeong Kim·Seungho Song
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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.

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Dohyeong Kim, Seungho Song. 2024-10-04. Bertrand's and Rodriguez Villegas' conjecture for real multi-quadratic Galois extensions of the rationals. https://arxiv.org/abs/2410.03238

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