Nous présentons une bibliographie d'articles récents sur les bornes inférieures des
discriminants de corps de nombres et sur des sujets voisins. Nous discutons quelques unes …

One of the classical problems in algebraic number theory, going back among others to
Dedekind [De78], Hensel [He08], and Hasse [Ha63], is to decide if an algebraic number field …

Let $ f (x)={x^ 5}+ p {x^ 3}+ q {x^ 2}+ rx+ s $ be an irreducible polynomial of degree 5 with
rational coefficients. An explicit resolvent sextic is constructed which has a rational root if …

This paper finds that all known parametric families of units in real quadratic, cubic, quartic
and sextic fields with prime conductor are linear combinations of Gaussian periods and …

The class numbers $ h_ {l}^{+} $ of the real cyclotomic fields $\mathbf {Q}(\zeta _ {l}^{}+\zeta
_ {l}^{-1}) $ are notoriously hard to compute. Indeed, the number $ h_ {l}^{+} $ is not known …

It is often the case that a Selmer group of an abelian variety and a group related to an ideal
class group can both be naturally embedded into the same cohomology group. One hopes …

We use the hypergeometric method to solve three families of Thue inequalities of degree 3,
4 and 6, respectively, each of which is parametrized by an integral parameter. We obtain …

Using" fast" algorithms for power series inversion (based on the fast Fourier transform and
multisectioning of power series), we have calculated all irregular primes up to one million …

We produce new examples of totally imaginary infinite extensions of $\mathbb {Q} $ which
have undecidable first-order theory by generalizing the methods used by Martínez-Ranero …

The term “simplest” field has been used to describe certain totally real, cyclic number fields
of degrees 2, 3, 4, 5, 6, and 8. For each of these degrees, the fields are defined by a one …