On the height of some generators of galois extensions with big galois group

2024/03/01 by Jenvrin, Jonathan
#11G50 #11R32 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2403.00500

Abstract

We study the height of generators of Galois extensions of the rationals having the alternating group \mathfrakA_n as Galois group. We prove that if such generators are obtained from certain, albeit classical, constructions, their height tends to infinity as n increases. This provides an analogue of a result by Amoroso, originally established for the symmetric group.

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