Effective approximation of algebraic numbers, d'après Enrico Bombieri
Effective diophantine approximation on
Effective irrationality measures and approximation by algebraic conjugates
Effective results for linear equations in two unknowns from a multiplicative division group
Effective results for restricted rational approximation to quadratic irrationals
Effective simultaneous approximation of complex numbers by conjugate algebraic integers
We study effectively the simultaneous approximation of n-1 different complex numbers by conjugate algebraic integers of degree n over ℤ(√-1). This is a refinement of a result of Motzkin [2] (see also [3], p. 50) who has no estimate for the remaining conjugate. If the n-1 different complex numbers lie symmetrically about the real axis, then ℤ(√-1) can be replaced by ℤ. In Section 1 we prove an effective version of a Kronecker approximation theorem; we start with an idea of H....
Effective solution of the D(-1)-quadruple conjecture
Equations diophantiennes exponentielles
Exceptional units and cyclic resultants
Exceptional units and numbers of small Mahler measure.
Extensions of the Cugiani-Mahler theorem
In 1955, Roth established that if is an irrational number such that there are a positive real number and infinitely many rational numbers with and , then is transcendental. A few years later, Cugiani obtained the same conclusion with replaced by a function that decreases very slowly to zero, provided that the sequence of rational solutions to is sufficiently dense, in a suitable sense. We give an alternative, and much simpler, proof of Cugiani’s Theorem and extend it to simultaneous...