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

Eva Bayer Fluckiger, Piotr Aleksander Maciak
2013
Article

Résumé

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

Source officielle

https://infoscience.epfl.ch/record/191036?ln=fr

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Moments of the number of points in a bounded set for number field lattices

Maryna Viazovska, Nihar Prakash Gargava, Vlad Serban

We examine the moments of the number of lattice points in a fixed ball of volume

V

for lattices in Euclidean space which are modules over the ring of integers of a number field

K

. In particular, denoting by

ω_K

the number of roots of unity in

K

, we ...

arXiv2023

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

Moments of the number of points in a bounded set for number field lattices

Lattice packings through division algebras

Fourier non-uniqueness sets from totally real number fields

Fourier non-uniqueness sets from totally real number fields

Lattice packings through division algebras

Moments of the number of points in a bounded set for number field lattices