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arXiv · 2410.03242

Bertrand's and Rodriguez Villegas' Conjecture for real quartic 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. For the exterior square case of totally real quartic extensions of the rationals, Costa and Friedman gave a lower bound of 0.802. We prove that the bound can be improved to 1.134 when the extension is further assumed to be Galois.

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Dohyeong Kim, Seungho Song. 2024-10-04. Bertrand's and Rodriguez Villegas' Conjecture for real quartic Galois extensions of the rationals. https://arxiv.org/abs/2410.03242

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