2022/06/30 by Denis Simon, Simon, Denis, Lea Terracini +1
Mathematics · #11G50 #11H31 #11R27 #11R33 #11Y40 #Advanced Topology and Set Theory #Algebraic number #Algebraic number field #Analytic Number Theory Research #Computer science #Connection (principal bundle) #Discrete mathematics #FOS: Mathematics #Field (mathematics) #Geometry #Ideal (ethics) #Integer (computer science) #Lattice (music) #Law #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Number Theory (math.NT) #Physics #Pure mathematics #math.NT #msc:11G50 #msc:11H31 #msc:11R27 #msc:11R33 #msc:11Y40
paper · pdf · doi:10.48550/arxiv.2206.15278
published in arXiv (Cornell University) (Cornell University)
arxiv created 2022/06/30 · openalex publication_date 2022/06/30 · arxiv updated 2022/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.