Negatively reduced ideals in orders of real quadratic fields: even discriminants
New computations concerning the Cohen-Lenstra heuristics.
New formulas for the class number of imaginary quadratic fields
New prime-producing quadratic polynomials associated with class number one or two.
Nombres de classes des corps quadratiques imaginaires
Nombres de classes et formes modulaires de poids 3/2.
Nombres de Hurwitz et régularité des idéaux premiers
Nombres de Hurwitz et unités elliptiques. Un critère de régularité pour les extensions abéliennes d'un corps quadratique imaginaire
Norm form equations and continued fractions.
Norms from certain extensions of
Norms from Quadratic Fields and Their Relation to Noncommuting 2 x 2 Matrices III. A Link between the 4-rank of the Ideal Class Groups in...(..m) and in ...(...-m).
Norms in Quadratic Fields and Their Relations to Non Commuting 2x2 Matrices I.
Northcott's theorem on heights II. The quadratic case
Note on primes of type x2 + 32y2, class number, and residuacity.
Note on the class-number of the maximal real subfield of a cyclomatic field.
Note on the congruence of Ankeny-Artin-Chowla type modulo p²
The results of [2] on the congruence of Ankeny-Artin-Chowla type modulo p² for real subfields of of a prime degree l is simplified. This is done on the basis of a congruence for the Gauss period (Theorem 1). The results are applied for the quadratic field ℚ(√p), p ≡ 5 (mod 8) (Corollary 1).
Note on the Hilbert 2-class field tower
Let be a number field with a 2-class group isomorphic to the Klein four-group. The aim of this paper is to give a characterization of capitulation types using group properties. Furthermore, as applications, we determine the structure of the second 2-class groups of some special Dirichlet fields , which leads to a correction of some parts in the main results of A. Azizi and A. Zekhini (2020).
Notes on small class numbers
Numbers with all factorizations of the same length in a quadratic number field