Invariants numériques des groupes de Hilbert.
Jacobi symbols, ambiguous ideals, and continued fractions
The purpose of this paper is to generalize some seminal results in the literature concerning the interrelationships between Legendre symbols and continued fractions. We introduce the power of ideal theory into the arena. This allows significant improvements over the existing results via the infrastructure of real quadratic fields.
K-groups and ideal class groups of number fields.
Knebusch-Milnor exact sequence and parity of class numbers
Kongruenzen zwischen Koeffizienten trigonometrischer Reihen und Klassenzahlen quadratisch imaginärer Körper.
Kuroda's class number formula
Kurzer Beweis des Diskriminantensatzes
Lengths of irreducible factorizations in fields with small class number
Les discriminants quadratiques et la congruence de Stickelberger
Les extensions quadratiques dur corps des raionnels, ou du corps de Gauss, ou du corps des racines cubiques de l'unité des calibres 1.
L-functions at the origin and annihilation of class groups in multiquadratic extensions
Lower bound for class numbers of certain real quadratic fields
Let be a square-free positive integer and be the class number of the real quadratic field We give an explicit lower bound for , where . Ankeny and Chowla proved that if is a natural number and is a square-free integer, then whenever . Applying our lower bounds, we show that there does not exist any natural number such that . We also obtain a similar result for the family . As another application, we deduce some criteria for a class group of prime power order to be cyclic.
Lower bounds for relative class numbers of imaginary abelian number fields and CM-fields
Lower bounds for the principal genus of definite binary quadratic forms.
Mahler measure of the Horie unit and Weber's class number problem in the cyclotomic ℤ₃-extension of ℚ
Majoration au point 1 des fonctions L associées aux caractères de Dirichlet primitifs, ou au caractère d'une extension quadratique d'un corps quadratique imaginaire principal.
Making sense of capitulation: reciprocal primes
Let ℓ be a rational prime, K be a number field that contains a primitive ℓth root of unity, L an abelian extension of K whose degree over K, [L:K], is divisible by ℓ, a prime ideal of K whose ideal class has order ℓ in the ideal class group of K, and any generator of the principal ideal . We will call a prime ideal of K ’reciprocal to ’ if its Frobenius element generates for every choice of . We then show that becomes principal in L if and only if every reciprocal prime is not a norm inside...
Maximal unramified extensions of imaginary quadratic number fields of small conductors
We determine the structures of the Galois groups Gal of the maximal unramified extensions of imaginary quadratic number fields of conductors under the Generalized Riemann Hypothesis). For all such , is , the Hilbert class field of , the second Hilbert class field of , or the third Hilbert class field of . The use of Odlyzko’s discriminant bounds and information on the structure of class groups obtained by using the action of Galois groups on class groups is essential. We also use class...
Minoration au point 1 des fonctions L et détermination des corps sextiques abéliens totalement imaginaires principaux
Minorations de discriminants