• On the height of some generato...

Treffer: On the height of some generators of Galois extensions with big Galois group

Title:
On the height of some generators of Galois extensions with big Galois group
Authors:
Jonathan Jenvrin
Contributors:
Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)
Source:
Journal of Number Theory. 269:78-105
Publication Status:
Preprint
Publisher Information:
Elsevier BV, 2025.
Publication Year:
2025
Subject Terms:
11R32, Mathematics - Number Theory, Height bounds, 11G50, 11R32, Galois extensions, MSC: 11G50, FOS: Mathematics, Alternating group, Lehmer Conjecture, Number Theory (math.NT), [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
Document Type:
Fachzeitschrift Article
Language:
English
ISSN:
0022-314X
DOI:
10.1016/j.jnt.2024.10.004
DOI:
10.48550/arxiv.2403.00500
Access URL:
http://arxiv.org/abs/2403.00500
Rights:
Elsevier TDM
CC 0
PDM
Accession Number:
edsair.doi.dedup.....705ff7a31c5a83d7df69bbfdee6a69ab
Database:
OpenAIRE

Weitere Informationen

We study the height of generators of Galois extensions of the rationals having the alternating group $\mathfrak{A}_n$ 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.
Final version, to appear in the Journal of Number Theory (JNTH)