On the enumeration of quintic fields with small discriminant.
On the equivariant main conjecture of Iwasawa theory
On the equivariant Tamagawa number conjecture for Abelian extensions of a quadratic imaginary field.
On the equivariant Tamagawa number conjecture for Tate motives. II.
On the Euclidean minimum of some real number fields
General methods from [3] are applied to give good upper bounds on the Euclidean minimum of real quadratic fields and totally real cyclotomic fields of prime power discriminant.
On the existence of cusp forms over function fields.
On the existence of dimension zero divisors in algebraic function fields defined over
On the existence of Minkowski units in totally real cyclic fields
Let be a totally real cyclic number field of degree that is the product of two distinct primes and such that the class number of the -th cyclotomic field equals 1. We derive certain necessary and sufficient conditions for the existence of a Minkowski unit for .
On the exponent of the ideal class groups of imaginary extensions of
On the extension of the Diophantine pair in .
On the Factorization of p-adic L-series.
On the Factorization of the Relative Class Number in Terms of Frobenius Divisions.
On the finiteness of for motives associated to modular forms.
On the fractional parts of the natural powers of a fixed number.
On the Functional Equation of the Artin L-Function for Characters of Real Representations.
On the fundamental periods of automorphic forms of arithmetic type.
On the fundamental unit and class number of certain quadratic functin fields, I
On the fundamental units of some cubic orders generated by units
Let ϵ be a totally real cubic algebraic unit. Assume that the cubic number field ℚ(ϵ) is Galois. Let ϵ, ϵ' and ϵ'' be the three real conjugates of ϵ. We tackle the problem of whether {ϵ,ϵ'} is a system of fundamental units of the cubic order ℤ[ϵ,ϵ',ϵ'']. Given two units of a totally real cubic order, we explain how one can prove that they form a system of fundamental units of this order. Several explicit families of totally real cubic orders defined by parametrized families of cubic 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 groups of cubics and trinomials