Large Algebraic Integers

Large Algebraic Integers

An algebraic integer is said large if all its real or complex embeddings have absolute value larger than $1$. An integral ideal is said \emph{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 re...

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Veröffentlicht in:International journal of number theory 2023-10, Vol.19 (9), p.2197-2214
Hauptverfasser: Simon, Denis, Terracini, Lea
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Mathematics
Mathematics - Number Theory
Number Theory
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container_title International journal of number theory
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creator Simon, Denis
Terracini, Lea
description An algebraic integer is said large if all its real or complex embeddings have absolute value larger than $1$. An integral ideal is said \emph{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.
doi_str_mv 10.48550/arxiv.2206.15278
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subjects Mathematics
Mathematics - Number Theory
Number Theory
title Large Algebraic Integers
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