On the Construction of Primitive Elements in Field Extensions.
On the Corestriction of Central Simple Algebras.
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 the Jordan-Kronecker's “Principle of reduction” for inseparable polynomials“”
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 number of real roots of a solvable polynomial
On the Pythagorean hull of Q.
The purpose of this paper is to prove that the Pythagorean hull of Q is the splitting field in R of a special set of rational polynomials.
On the semi-simplicity of Galois actions
On Torsion Points of Formal Groups over a Ring of Witt Vectors.
On trace forms of hilbertian fields.