Quelques propriétés des corps cycliques de degré 4
Racines cubiques de nombres entiers et multiplication complexe dans les fonctions elliptiques
Ramification in quartic cyclic number fields generated by
If is the splitting field of the polynomial and is a rational prime of the form , we give appropriate generators of to obtain the explicit factorization of the ideal , where is a positive rational prime. For this, we calculate the index of these generators and integral basis of certain prime ideals.
Ranks of 3-class groups of non-Galois cubic fields
Rational quartic reciprocity
Rational quartic reciprocity II
Real zeros of the Dedekind zeta function of an imaginary quadratic field
Recherches analytiques sur la surface du troisième ordre qui est la réciproque de la surface de Steiner
Relative integral basis for algebraic number fields.
Representation of primes by the principal form of discriminant -D when the classnumber h(-D) is 3
Simplest Cubic Fields.
Solutions to xyz = 1 and x + y + z = k in algebraic integers of small degree, II
Let k ∈ ℤ be such that is finite, where . We complete the determination of all solutions to xyz = 1 and x + y + z = k in integers of number fields of degree at most four over ℚ.
Some quartic number fields containing an imaginary quadratic subfield
Let ε be a quartic algebraic unit. We give necessary and sufficient conditions for (i) the quartic number field K = ℚ(ε) to contain an imaginary quadratic subfield, and (ii) for the ring of algebraic integers of K to be equal to ℤ[ε]. We also prove that the class number of such K's goes to infinity effectively with the discriminant of K.
Some reults on fundamental units in cubic fields.
Sur la capitulation des 2-classes d'idéaux de 𝕜 = ℚ (√(2pq),i) où p ≡ -q ≡ 1 mod 4
Sur la constante de Lenstra des corps de nombres
Sur le groupe des unités de corps de nombres de degré et
Nous déterminons sous certaines hypothèses, un système fondamental d’unités du corps non pur et de son sous-corps quadratique, où est solution du polynômeavec , , , , , non nuls.
Tame kernels of cubic cyclic fields
The 2-class group of certain biquadratic number fields.
The Arithmetic Genus of the Hubert Modular Variety and the Elliptic Fixed Points of the Hilbert Modular Group.