Counting Bounded Elements of a Number Field-Reference-Cited by-同舟云学术

Counting Bounded Elements of a Number Field

Published:2020-06-18 Issue:1 Volume:2022 Page:373-390
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Fraczyk Mikołaj¹²³,Harcos Gergely¹⁴⁵,Maga Péter¹⁴

Affiliation:

1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, POB 127, Budapest H-1364, Hungary

2. MTA Rényi Intézet Lendület Groups and Graphs Research Group

3. Institute for Advanced Study, Princeton, NJ, USA

4. MTA Rényi Intézet Lendület Automorphic Research Group

5. Central European University, Nador u. 9, Budapest H-1051, Hungary

Abstract

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.

Funder

European Research Council

National Research, Development and Innovation Office

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/article-pdf/2022/1/373/42136518/rnaa126.pdf

Reference16 articles.

1. Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves;Bhargava;J. Amer. Math. Soc.

2. Notes on geometry of numbers. The October meeting of the San Francisco section;Blichfeldt;Bull. Amer. Math. Soc.,1921

3. Finite permutation groups and finite simple groups;Cameron;Bull. London Math. Soc.,1981

4. Verallgemeinerung einer Mordellschen Beweismethode in der Geometrie der Zahlen;van der Corput;Acta Arith.,1935

5. Triangulations: Structures for Algorithms and Applications;De Loera,2010

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