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
O jedenáctém a dvanáctém Hilbertově problému
On -class field towers of imaginary quadratic number fields
For a number field , let denote its Hilbert -class field, and put . We will determine all imaginary quadratic number fields such that is abelian or metacyclic, and we will give in terms of generators and relations.
On a problem of Eisenstein
On Birch and Swinnerton-Dyer's conjecture for elliptic curves with complex multiplication. I
On certain continued fraction expansions of fixed period length
On certain infinite families of imaginary quadratic fields whose Iwasawa λ-invariant is equal to 1
Let p be an odd prime number. We prove the existence of certain infinite families of imaginary quadratic fields in which p splits and for which the Iwasawa λ-invariant of the cyclotomic ℤₚ-extension is equal to 1.
On CM-fields with the same maximal real subfield
On cyclotomic ℤ ₚ-extensions of real quadratic fields
On -polynomials with integer coefficients
We give a family of -polynomials with integer coefficients whose splitting fields over are unramified cyclic quintic extensions of quadratic fields. Our polynomials are constructed by using Fibonacci, Lucas numbers and units of certain cyclic quartic fields.
On diophantine equations involving sums of powers with quadratic characters as coefficients, II
On Eisenstein's problem
On elementary abelian 2-Sylow K₂ of rings of integers of certain quadratic number fields
A large number of papers have contributed to determining the structure of the tame kernel of algebraic number fields F. Recently, for quadratic number fields F whose discriminants have at most three odd prime divisors, 4-rank formulas for have been made very explicit by Qin Hourong in terms of the indefinite quadratic form x² - 2y² (see [7], [8]). We have made a successful effort, for quadratic number fields F = ℚ (√(±p₁p₂)), to characterize in terms of positive definite binary quadratic forms,...
On expansions of Gaussian integers with non-negative digits.
On extensions of 1 chains