On Hilbert-Speiser type imaginary quadratic fields
On integral representations by totally positive ternary quadratic forms
Let be a totally real algebraic number field whose ring of integers is a principal ideal domain. Let be a totally definite ternary quadratic form with coefficients in . We shall study representations of totally positive elements by . We prove a quantitative formula relating the number of representations of by different classes in the genus of to the class number of , where is a constant depending only on . We give an algebraic proof of a classical result of H. Maass on representations...
On K2 (...) and presentations of SLn (...) in the real quadratic case.
On numbers with a unique representation by a binary quadratic form
On p-Adic L-Functions over Real Quadratic Fields.
On power residue characters of units and the representation of numbers by quadratic forms
On real quadratic number fields suitable for cryptography.
On reciprocity equivalence of quadratic number fields
On representations of numbers by sums of squares and quadratic fields
On shifted primes
On some class-fields related to primes of type x2 + 32y2.
On some imaginary triquadratic number fields with or
Let be a square free integer and . In the present work we determine all the fields such that the -class group, , of is of type or .
On some metabelian 2-groups and applications I
Let G be some metabelian 2-group satisfying the condition G/G’ ≃ ℤ/2ℤ × ℤ/2ℤ × ℤ/2ℤ. In this paper, we construct all the subgroups of G of index 2 or 4, we give the abelianization types of these subgroups and we compute the kernel of the transfer map. Then we apply these results to study the capitulation problem for the 2-ideal classes of some fields k satisfying the condition , where is the second Hilbert 2-class field of k.
On Sylow 2-subgroups of K2OF for quadratic number fields F.
On Tate-Shafarevich groups of .
On the -class group of some number fields with large degree
Let be an odd square-free integer, any integer and . In this paper, we shall determine all the fields having an odd class number. Furthermore, using the cyclotomic -extensions of some number fields, we compute the rank of the -class group of whenever the prime divisors of are congruent to or .
On the 2-primary part of a conjecture of Birch and Tate
On the 2-Sylow subgroup of the Hilbert kernel of of number fields
On the 4-rank of ideal class groups of quadratic function fields
On the Asymptotic Behaviour of the Ideal Counting Function in Quadratic Number Fields.