On the quadriquadric Curve in connexion with the theory of Elliptic Functions
On the quantitative unit sum number problem-an application of the subspace theorem
On the quartic character of quadratic units.
On the Rational Points of Abelian Varieties over Zp Extensions of Number Fields.
On the real cohomology of arithmetic groups and the rank conjecture for number fields
On the Real Points of an Arithmetic Quotient of a Bounded Symmetrie Domain.
On the reducibility type of trinomials
On the regularity and rationality of certain elements of finite order in Lie groups.
On the relation between two conjectures on polynomials
On the relation between units and Jacobi sums in Prime cyclotomic Fields.
On the relative class number of cyclotomic function fields
On the representation of units by cyclotomic polynomials
On the Resolution of Cusp Singularities and the Shintani Decomposition in Totally Real Cubic Number Fields.
On the resolution of index form equations in dihedral quartic number fields.
On the Riemann-Roch theorem for orders in the ring of valuation vectors of a function field.
On the ring of -integers of a cyclic -extension over a number field
Let be a prime number. A finite Galois extension of a number field with group has a normal -integral basis (-NIB for short) when is free of rank one over the group ring . Here, is the ring of -integers of . Let be a power of and a cyclic extension of degree . When , we give a necessary and sufficient condition for to have a -NIB (Theorem 3). When and , we show that has a -NIB if and only if has a -NIB (Theorem 1). When divides , we show that this descent property...
On the Saito-Kurokawa Lifting.
On the Self-Duality of a Ring of Integers as a Galois Module.
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...
On the Shafarevich and Tate conjectures for hyperkähler varieties.