14 citations · 30 across the 6 of their papers we have counts for
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Diophantine approximation in small degree
Damien Roy
We discuss the problem of finding optimal exponents in Diophantine estimates involving one real number and, in some cases where such an exponent is known, present some properties o…
A Gel'fond type criterion in degree two
Benoit Arbour, Damien Roy
We establish a criterion for a complex number to be algebraic over Q of degree at most two. It requires that, for any sufficiently large real number X, there exists a non-zero poly…
Approximation simultanée d'un nombre et de son carré [Simultaneous approximation to a real number and its square]
Damien Roy
In 1969, H. Davenport and W. Schmidt established a measure of simultaneous approximation for a real number ξand its square by rational numbers with the same denominator, assuming o…
Approximation to real numbers by cubic algebraic integers II
Damien Roy
It has been conjectured for some time that, for any integer n\ge 2, any real number ε>0 and any transcendental real number ξ, there would exist infinitely many algebraic integers α…
Approximation to real numbers by cubic algebraic integers I
Damien Roy
In 1969, H. Davenport and W. M. Schmidt studied the problem of approximation to a real number ξby algebraic integers of degree at most three. They did so, using geometry of numbers…
Diophantine approximation by conjugate algebraic integers
Damien Roy, Michel Waldschmidt
Building on work of Davenport and Schmidt, we mainly prove two results. The first one is a version of Gel'fond's transcendence criterion which provides a sufficient condition for a…