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
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