On unit solutions of the equation xyz=x+y+z in a number field with unit group of rank 1
On units and fundamental units.
On Unramified Galois Extensions Over Maximum Abelian Extensions of Algebraic Number Fields.
On valued function fields II. Regular functions and elements with the uniqueness property.
On values of L-functions of totally real algebraic number fields at integers
On values of the Mahler measure in a quadratic field (solution of a problem of Dixon and Dubickas)
On Values of Zeta Functions and ?-adic Euler Characteristc.
On Waring's problem in algebraic number fields
On Waring's problem in algebraic number fields
On Washington group of circular units of some composita of quadratic fields
On wild ramification in quaternion extensions
This paper provides a complete catalog of the break numbers that occur in the ramification filtration of fully and thus wildly ramified quaternion extensions of dyadic number fields which contain (along with some partial results for the more general case). This catalog depends upon the refined ramification filtration, which as defined in [2] is associated with the biquadratic subfield. Moreover we find that quaternion counter-examples to the conclusion of the Hasse-Arf Theorem are extremely rare...
On zeroes of the twisted tensor L-function.
Optimality of the Width- Non-adjacent Form: General Characterisation and the Case of Imaginary Quadratic Bases
We consider digit expansions with an endomorphism of an Abelian group. In such a numeral system, the -NAF condition (each block of consecutive digits contains at most one nonzero) is shown to minimise the Hamming weight over all expansions with the same digit set if and only if it fulfills the subadditivity condition (the sum of every two expansions of weight admits an optimal -NAF).This result is then applied to imaginary quadratic bases, which are used for scalar multiplication in elliptic...
Orders, in non-Eichler (R)-algebras over global function fields, having the cancellation property.
Orders in quaternion algebras.
Orders of a quaternion algebra over a number field.
Orders of quadratic extensions of number fields
Orders with a normal basis
Ordinary -adic Eisenstein series and -adic -functions for unitary groups
The purpose of this work is to carry out the first step in our four-step program towards the main conjecture for by the method of Eisenstein congruence on , where is an imaginary quadratic field. We construct a -adic family of ordinary Eisenstein series on the group of unitary similitudes with the optimal constant term which is basically the product of the Kubota-Leopodlt -adic -function and a -adic -function for . This construction also provides a different point of view of -adic...
Ordre de Bruhat et transfert : le cas réel