On the imbeddings of imaginary quadratic orders in definite quaternion orders.
On the indices of multiquadratic 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 integral basis of the maximal real subfield of a cyclotomic field.
On the ?-invariant of the ?-transform of a rational function.
On the irreducibility of 0,1-polynomials of the form f(x)xⁿ + g(x)
If f(x) and g(x) are relatively prime polynomials in ℤ[x] satisfying certain conditions arising from a theorem of Capelli and if n is an integer > N for some sufficiently large N, then the non-reciprocal part of f(x)xⁿ + g(x) is either identically ±1 or is irreducible over the rationals. This result follows from work of Schinzel in 1965. We show here that under the conditions that f(x) and g(x) are relatively prime 0,1-polynomials (so each coefficient is either 0 or 1) and f(0) = g(0) = 1, one...
On the irreducibility of -quadrinomials.
On the irreducibility of a class of polynomials, IV
On the irreducibility of neighbouring polynomials
On the irreducibility of the generalized Laguerre polynomials
On the Iwasaw ...-invariants of certain families of real quadratic fields.
On the Iwasawa invariants of certain -extensions
On the iwasawa invariants of totally real number fields.
On the Iwasawa theory of CM elliptic curves at supersingular primes
On the Iwasawa λ-invariants of quaternion extensions
On the Iwasawa λ-invariants of real quadratic fields
On the jacobian variety of some algebraic curves
On the K-Theory of Algebraically Closed Fields.
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 Lagrange resolvents of a dihedral quintic polynomial.