Jean-Paul Cerri

Euclidean minima of totally real number fields: Algorithmic determination

This article deals with the determination of the Euclidean minimum

EUCLIDEAN TOTALLY DEFINITE QUATERNION FIELDS OVER THE RATIONAL FIELD AND OVER QUADRATIC NUMBER FIELDS

M(K)

Some generalized Euclidean and 2-stage Euclidean number fields that are not norm-Euclidean

of a totally real number field

Euclidean minima and central division algebras

K

Spectres euclidiens et inhomogènes des corps de nombres

of degree

Computation of Euclidean minima in totally definite quaternion fields

n\geq 2

Totally indefinite Euclidean quaternion fields

, using techniques from the geometry of numbers. Our improvements of existing algorithms allow us to compute Euclidean minima for fields of degree

New Results - Class groups and other invariants ofnumber fields

2

Research Program - Number fields, class groups and other invariants

to

New Results - Quaternion algebras

8