On cyclotomic ℤ ₚ-extensions of real quadratic fields
On cyclotomic polynomials with coefficients.
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 so that .
On sot hat represents and and not .
On Davenport's bound for the degree of f³ - g² and Riemann's Existence Theorem
On decimal and continued fraction expansions of a real number
On Dedekind domains in infinite algebraic extensions
On Dedekind's criterion and monogenicity over Dedekind rings.
On deformation of maximally degenerate stable marked curves and Oda's problem.
On degrees of three algebraic numbers with zero sum or unit product
Let α, β and γ be algebraic numbers of respective degrees a, b and c over ℚ such that α + β + γ = 0. We prove that there exist algebraic numbers α₁, β₁ and γ₁ of the same respective degrees a, b and c over ℚ such that α₁ β₁ γ₁ = 1. This proves a previously formulated conjecture. We also investigate the problem of describing the set of triplets (a,b,c) ∈ ℕ³ for which there exist finite field extensions K/k and L/k (of a fixed field k) of degrees a and b, respectively, such that the degree of the...
On delta sets and their realizable subsets in Krull monoids with cyclic class groups
Let M be a commutative cancellative monoid. The set Δ(M), which consists of all positive integers which are distances between consecutive factorization lengths of elements in M, is a widely studied object in the theory of nonunique factorizations. If M is a Krull monoid with cyclic class group of order n ≥ 3, then it is well-known that Δ(M) ⊆ {1,..., n-2}. Moreover, equality holds for this containment when each class contains a prime divisor from M. In this note, we consider the question of determining...
On Demuskin groups with involution
On density modulo 1 of some expressions containing algebraic integers
On determination of GL₃ cusp forms
On determining the quadratic subfields of -extensions of complex quadratic fields
On diagonal cubic surfaces.
On diameters of algebraic integers
On difference sets of sets of integers
On difference sets of sets of positive integers