Research PaperNo Access

Large algebraic integers

Denis Simon

Université de Caen-Normandie, CNRS, Laboratoire de Mathématiques Nicolas Oresme, 14000 Caen, France

E-mail Address: [email protected]

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and

Lea Terracini

Università di Torino, Dipartimento di Informatica, 10143 Torino, Italia

E-mail Address: [email protected]

Corresponding author

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https://doi.org/10.1142/S1793042123501075Cited by:0 (Source: Crossref)

Abstract

An algebraic integer is said large if all its real or complex embeddings have absolute value larger than $1$ . An integral ideal is said large if it admits a large generator. We investigate the notion of largeness, relating it to some arithmetic invariants of the field involved, such as the regulator and the covering radius of the lattice of units. We also study its connection with the Weil height and the Bogomolov property. We provide an algorithm for testing largeness and give some applications to the construction of floor functions arising in the theory of continued fractions.

Keywords:

AMSC: 11H31, 11R27, 11R33, 11Y40, 11G50

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