On Euclidean rings of integers in cyclotomic fields.
On expansions of Gaussian integers with non-negative digits.
On extensions of 1 chains
On intervals containing full sets of conjugates of algebraic integers
On K-Stage Euclidean algorithms for Galois extensions of Q.
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 power residues
On sequences of algebraic integers in pure extensions of prime degree
On Shioda's problem about Jacobi sums
On Shioda's problem about Jacobi sums II
On the classification of hermitian forms. I. Rings of algebraic integers
On the common index divisors of a dihedral field of prime degree.
On the fractional parts of the natural powers of a fixed number.
On the height of algebraic numbers with real conjugates
On the K-theory of the -algebra generated by the left regular representation of an Ore semigroup
We compute the -theory of -algebras generated by the left regular representation of left Ore semigroups satisfying certain regularity conditions. Our result describes the -theory of these semigroup -algebras in terms of the -theory for the reduced group -algebras of certain groups which are typically easier to handle. Then we apply our result to specific semigroups from algebraic number theory.
On the non-torsion elements in the algebraic K-theory of rings of integers.
On the number of ideals free from large prime divisors.
On the product of the conjugates outside the unit circle of an algebraic integer
On the product of the conjugates outside the unit circle of an algebraic number
On the S-Euclidean minimum of an ideal class
We show that the S-Euclidean minimum of an ideal class is a rational number, generalizing a result of Cerri. In the proof, we actually obtain a slight refinement of this and give some corollaries which explain the relationship of our results with Lenstra's notion of a norm-Euclidean ideal class and the conjecture of Barnes and Swinnerton-Dyer on quadratic forms. In particular, we resolve a conjecture of Lenstra except when the S-units have rank one. The proof is self-contained but uses ideas from...