On the Construction of Galois Extensions of Function Fields and Number Fields.
On the Construction of Primitive Elements in Field Extensions.
On the convergence of Halley-like method.
On the Corestriction of Central Simple Algebras.
On the degree of an irreducible factor of the Bernoulli polynomials
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 Diophantine equation f(y) - x = 0
On the distribution of Galois groups. II.
On the distribution of the number of real zeros of a random polynomial.
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 enumeration of quintic fields with small discriminant.
On the equation
On the extension of a valuation on a field to . - II
On the Extension of Real Places
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 fourth order root finding methods of Euler's type.
On the Fundamental Theorem of Algebra
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.