Counting bounded elements of a number field
Number Theory
2024-11-18 v3
Abstract
We estimate, in a number field, the number of elements and the maximal number of linearly independent elements, with prescribed bounds on their valuations. As a by-product, we obtain new bounds for the successive minima of ideal lattices. Our arguments combine group theory, ramification theory, and the geometry of numbers.
Keywords
Cite
@article{arxiv.1907.01116,
title = {Counting bounded elements of a number field},
author = {Mikołaj Frączyk and Gergely Harcos and Péter Maga},
journal= {arXiv preprint arXiv:1907.01116},
year = {2024}
}
Comments
11 pages, LaTeX2e; v2: updated Corollary 3 and added Corollary 4; v3: revised version incorporating suggestions by the referees (the main changes are in the title and in the Introduction, e.g. Corollary 1 and the paragraph below Theorem 4 are new)