On some characterizations of the complex number field
On subfields of
On the Beckmann-Black problem
On the class numbers of certain Hilbert class fields.
On the compositum of all degree extensions of a number field
We study the compositum of all degree extensions of a number field in a fixed algebraic closure. We show contains all subextensions of degree less than if and only if . We prove that for there is no bound on the degree of elements required to generate finite subextensions of . Restricting to Galois subextensions, we prove such a bound does not exist under certain conditions on divisors of , but that one can take when is prime. This question was inspired by work of Bombieri and...
On the computation of resolvents and Galois groups.
On the Computation of the Galois Group over the Quotient Field of C [...].
On the congruence , where q is a prime and f is a k-normal polynomial
On the Construction of Galois Extensions of Function Fields and Number Fields.
On the Construction of Primitive Elements in Field Extensions.
On the Corestriction of Central Simple Algebras.
On the dimension of the space of ℝ-places of certain rational function fields
We prove that for every n ∈ ℕ the space M(K(x 1, …, x n) of ℝ-places of the field K(x 1, …, x n) of rational functions of n variables with coefficients in a totally Archimedean field K has the topological covering dimension dimM(K(x 1, …, x n)) ≤ n. For n = 2 the space M(K(x 1, x 2)) has covering and integral dimensions dimM(K(x 1, x 2)) = dimℤ M(K(x 1, x 2)) = 2 and the cohomological dimension dimG M(K(x 1, x 2)) = 1 for any Abelian 2-divisible coefficient group G.
On the distribution of Galois groups. II.
On the distribution of the roots of polynomial
We consider the polynomial for which arises as the characteristic polynomial of the -generalized Fibonacci sequence. In this short paper, we give estimates for the absolute values of the roots of which lie inside the unit disk.
On the extension of a valuation on a field to . - II
On the extension of the Jordan-Kronecker's “Principle of reduction” for inseparable polynomials“”
On the extension of valuations on a field to . - I
On the Galois group of generalized Laguerre polynomials
Using the theory of Newton Polygons, we formulate a simple criterion for the Galois group of a polynomial to be “large.” For a fixed , Filaseta and Lam have shown that the th degree Generalized Laguerre Polynomial is irreducible for all large enough . We use our criterion to show that, under these conditions, the Galois group of is either the alternating or symmetric group on letters, generalizing results of Schur for .
On the Galois group of the generalized Fibonacci polynomial.
On the Galois spectra of polynomials with integral parameters.