Upper bounds for the Euclidean minima of abelian fields of odd prime power conductor

2013/10/22 by Eva Bayer‐Fluckiger, Eva Bayer-Fluckiger, Bayer-Fluckiger, Eva +2 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1310.6057

To appear in Mathematische Annalen

arxiv created 2013/10/22 · openalex publication_date 2013/10/22 · arxiv updated 2013/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to give upper bounds for the Euclidean minima of abelian fields of odd prime conductor. In particular, these bounds imply Minkowski's conjecture for totally real number fields of conductor p^r, where p is an odd prime and r is at least 2.

Cited by

• Upper bounds for the Euclidean minima of abelian number fields

Related

• Upper bounds for the Euclidean minima of abelian number fields
• On the Power of Integers and Conductors of Quadratic Fields
• Euclidean minima of algebraic number fields
• Explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields
• An Investigation Into Several Explicit Versions of Burgess' Bound