On a theorem of Bauer and some of its applications
On Elliptic Units and Class Number of a Certain Non-Galois Number Field.
On index formulas of Siegel units in a ring class field
On Kronecker équivalence of algebraic number fields.
On K-Stage Euclidean algorithms for Galois extensions of Q.
On octahedral extensions of and quadratic -curves
We give a necessary condition for a surjective representation Gal to arise from the -torsion of a -curve. We pay a special attention to the case of quadratic -curves.
On p-class groups of cyclic extensions of prime degree p of number fields
On power integral bases for certain pure number fields defined by
Let be a number field generated by a complex root of a monic irreducible polynomial , , is a square free rational integer. We prove that if or and , then the number field is monogenic. If or , then the number field is not monogenic.
On the arithmetic of two constructions of Salem numbers.
On the common index divisors of a dihedral field of prime degree.
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 genus group of algebraic number fields
On the Lagrange resolvents of a dihedral quintic polynomial.
On the nonessential discriminant divisor of an algebraic number field
On the theory of nth power residues and a conjecture of Kronecker