Publication

Upper bounds for Euclidean minima of algebraic number fields

Eva Bayer Fluckiger
2006
Journal Articles

Abstract

The aim of this paper is to give new upper bounds for Euclidean minima of algebraic number fields. In particular, to show that Minkowski's conjecture holds for the maximal totally real subfields of cyclotomic fields of prime power conductor.

Official source

https://infoscience.epfl.ch/entities/publication/713f75e7-8910-4331-9165-c802f01d1b01

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Eva Bayer Fluckiger
2006
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/713f75e7-8910-4331-9165-c802f01d1b01

About this result

Related concepts (19)

Quadratic field

In algebraic number theory, a quadratic field is an algebraic number field of degree two over , the rational numbers. Every such quadratic field is some where is a (uniquely defined) square-free integer different from and . If , the corresponding quadratic field is called a real quadratic field, and, if , it is called an imaginary quadratic field or a complex quadratic field, corresponding to whether or not it is a subfield of the field of the real numbers.

Algebraic number field

In mathematics, an algebraic number field (or simply number field) is an extension field of the field of rational numbers such that the field extension has finite degree (and hence is an algebraic field extension). Thus is a field that contains and has finite dimension when considered as a vector space over . The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.

Cyclotomic field

In number theory, a cyclotomic field is a number field obtained by adjoining a complex root of unity to Q, the field of rational numbers. Cyclotomic fields played a crucial role in the development of modern algebra and number theory because of their relation with Fermat's Last Theorem. It was in the process of his deep investigations of the arithmetic of these fields (for prime n) – and more precisely, because of the failure of unique factorization in their rings of integers – that Ernst Kummer first introduced the concept of an ideal number and proved his celebrated congruences.

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