Publication

Bounds for the Euclidean minima of function fields

Publications associées (29)

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Consider a diffusion field induced by a finite number of localized and instantaneous sources. In this paper, we study the problem of estimating these sources (including their intensities, spatial locations, and activation time) from the spatiotemporal samp ...

2011

Diagonal Quartic Surfaces And Transcendental Elements Of The Brauer Group

Evis Ieronymou

We exhibit central simple algebras over the function field of a diagonal quartic surface over the complex numbers that represent the 2-torsion part of its Brauer group. We investigate whether the 2-primary part of the Brauer group of a diagonal quartic sur ...

Cambridge University Press2010

Arithmetic Bounds-Lenstra's Constant and Torsion of K-Groups

Julien Houriet

This thesis is concerned with computations of bounds for two different arithmetic invariants. In both cases it is done with the intention of proving some algebraic or arithmetic properties for number fields. The first part is devoted to computations of low ...

EPFL2010

A counterexample to the local-global principle of linear dependence for Abelian varieties

Peter Simon Jossen, Antonella Perucca

Let A be an Abelian variety defined over a number field k. Let P be a point in A(k) and let X be a subgroup of A(k). Gajda and Kowalski asked in 2002 whether it is true that the point P belongs to X if and only if the point (P mod p) belongs to (X mod p) f ...

2010

Euclidean minima and central division algebras

Eva Bayer Fluckiger, Jérôme Chaubert

The notion of Euclidean minimum of a number field is a classical one. In this paper we generalize it to central division algebras and establish some general results in this new context. ...

2009

Two variants of the support problem for products of abelian varieties and tori

Antonella Perucca

Let G be the product of an abelian variety and a torus defined over a number field K. Let P and Q be K-rational points on G. Suppose that for all but finitely many primes p of K the order of (Q mod p) divides the order of (P mod p). Then there exist a K-en ...

2009

Statistics Of Prime Divisors In Function Fields

Robert Christopher Rhoades

We show that the prime divisors of a random polynomial in F-q[t] are typically "Poisson distributed". This result is analogous to the result in Z of Granville [1]. Along the way, we use a sieve developed by Granville and Soundararajan [2] to give a simple ...

2009

Upper bounds for Euclidean minima of algebraic number fields

Eva Bayer Fluckiger

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. ...

2006

Réseaux idéaux sur des corps CM et des corps totalement réels

Ivan Suarez Atias

This thesis deals with the study of ideal lattices over number fields. Let K be a number field, which is assumed to be CM or totally real. An ideal lattice over K is a pair (I,b), where I is a fractional ideal of K and b : I × I → R is a symmetric positive ...

EPFL2005