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.
On the Galois theory of difference fields.
On the Galois Theory of function fields of one variable over number fields.
On the infinite fern of Galois representations of unitary type
Let be a CM number field, an odd prime totally split in , and let be the -adic analytic space parameterizing the isomorphism classes of -dimensional semisimple -adic representations of satisfying a selfduality condition “of type ”. We study an analogue of the infinite fern of Gouvêa-Mazur in this context and show that each irreducible component of the Zariski-closure of the modular points in has dimension at least . As important steps, and in any rank, we prove that any first order...
On the inverse problem of Galois theory.
The problem of the construction of number fields with Galois group over Q a given finite groups has made considerable progress in the recent years. The aim of this paper is to survey the current state of this problem, giving the most significant methods developed in connection with it.
On the nonexcellence of field extensions .
On the Nonflatness of Analytic Tensor Product.