A remark on my paper "On the Saito-Kurokawa lifting".
A remark on primitive roots and ramitfication
A remark on real radical extensions
A remark on the zeta-function of an algebraic number field.
A Riemann-Hurwitz formula for the Selmer group of an elliptic curve with complex multiplication.
A Schinzel theorem on continued fractions in function fields
A self-similar tiling generated by the minimal Pisot number
A simple criterion for solvability of both and .
A simplification of the formula for L(1,χ) where χ is a totally imaginary Dirichlet character of a real quadratic field
A stably free and non-free ring of integers. (Un anneau d'entiers stablement libre et non libre.)
A Stark conjecture “over ” for abelian -functions with multiple zeros
Suppose is an abelian extension of number fields. Stark’s conjecture predicts, under suitable hypotheses, the existence of a global unit of such that the special values for all characters of can be expressed as simple linear combinations of the logarithms of the different absolute values of .In this paper we formulate an extension of this conjecture, to attempt to understand the values when the order of vanishing may be greater than one. This conjecture no longer predicts the existence...
A structure theorem for sets of lengths
A Study of Hasse-Witt Matrices by Local Methods.
A subconvexity bound for Hecke L-functions
A supplement to Scholz's reciprocity law
A survey of computational class field theory
We give a survey of computational class field theory. We first explain how to compute ray class groups and discriminants of the corresponding ray class fields. We then explain the three main methods in use for computing an equation for the class fields themselves: Kummer theory, Stark units and complex multiplication. Using these techniques we can construct many new number fields, including fields of very small root discriminant.
A System of Free Generators for the Universal even Ordinary Z(2) Distribution on Q2k-Z2k .
A Tate sequence for global units
A Terr algorithm for computations in the infrastructure of real-quadratic number fields
We show how to adapt Terr’s variant of the baby-step giant-step algorithm of Shanks to the computation of the regulator and of generators of principal ideals in real-quadratic number fields. The worst case complexity of the resulting algorithm depends only on the square root of the regulator, and is smaller than that of all other previously specified unconditional deterministic algorithm for this task.
A theorem of Mahler and some applications to transference theorems