Sur une classe de groupes d'ordre fini contenus dans les groupes linéaires
Sur une généralisation de la conjecture de Leopoldt
The calculation of large units in cyclic cubic fields.
The catenary degree of Krull monoids I
Let be a Krull monoid with finite class group such that every class contains a prime divisor (for example, a ring of integers in an algebraic number field or a holomorphy ring in an algebraic function field). The catenary degree of is the smallest integer with the following property: for each and each two factorizations of , there exist factorizations of such that, for each , arises from by replacing at most atoms from by at most new atoms. Under a very mild condition...
The diophantine equation x3 + dy3 = 1 and the fundamental unit of a pure cubic field Q (...d).
The distribution of the fundamental units of real quadratic fields
The equation xyz = x + y + z = 1 in integers of a cubic field.
The Iwasawa λ-invariants of ℤₚ-extensions of real quadratic fields
1. Introduction. Let k be a totally real number field. Let p be a fixed prime number and ℤₚ the ring of all p-adic integers. We denote by λ=λₚ(k), μ=μₚ(k) and ν=νₚ(k) the Iwasawa invariants of the cyclotomic ℤₚ-extension of k for p (cf. [10]). Then Greenberg’s conjecture states that both λₚ(k) and μₚ(k) always vanish (cf. [8]). In other words, the order of the p-primary part of the ideal class group of kₙ remains bounded as n tends to infinity, where kₙ is the nth layer of . We know by the Ferrero-Washington...
The Jacobi-Perron Algorithm and Pisot numbers
The number of different lengths of irreducible factorization of a natural number in an algebraic number field
The refined p-adic abelian Stark conjecture in function fields.
The Regulator Spectrum For Totally Real Cubic Fields.
The set of minimal distances in Krull monoids
Let H be a Krull monoid with class group G. Then every nonunit a ∈ H can be written as a finite product of atoms, say . The set (a) of all possible factorization lengths k is called the set of lengths of a. If G is finite, then there is a constant M ∈ ℕ such that all sets of lengths are almost arithmetical multiprogressions with bound M and with difference d ∈ Δ*(H), where Δ*(H) denotes the set of minimal distances of H. We show that max Δ*(H) ≤ maxexp(G)-2,(G)-1 and that equality holds if every...
The size of the fundamental solutions of consecutive Pell equations.
The unit group of some fields of the form
Let and be two different prime integers such that with , and a positive odd square-free integer relatively prime to and . In this paper we investigate the unit groups of number fields .
Théorème de Baker-Brumer sur les unités d'un corps de nombres algébriques
Theorie des genres analytique des fonctions L p-adiques des corps totalement réels.
Truncated Units in Infinitely many Algebraic Number Fields of Degree n...4.
Truncated units in the algebraic number field , where ,