On the Homomorphisms of the Integral Linear Groups.
On the ideal class groups of the maximal real subfields of number fields with all roots of unity
In this paper, for a totally real number field we show the ideal class group of is trivial. We also study the -component of the ideal class group of the cyclotomic -extension.
On the image of -adic Galois representations
We explore the question of how big the image of a Galois representation attached to a -adic modular form with no complex multiplication is and show that for a “generic” set of -adic modular forms (normalized, ordinary eigenforms with no complex multiplication), all have a large image.
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 irreducible factors of a polynomial over a valued field
We explicitly provide numbers , such that each irreducible factor of a polynomial with integer coefficients has a degree greater than or equal to and can have at most irreducible factors over the field of rational numbers. Moreover, we prove our result in a more general setup for polynomials with coefficients from the valuation ring of an arbitrary valued field.
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