On approximation to real numbers by algebraic numbers
On arithmetic properties of the convergents of Euler's number
On Baker type lower bounds for linear forms
A criterion is given for studying (explicit) Baker type lower bounds of linear forms in numbers over the ring of an imaginary quadratic field . This work deals with the simultaneous auxiliary functions case.
On Best Two-Dimensional Dirichlet-Approximations and their Algorithmic Calculation.
On commuting circle mappings and simultaneous Diophantine approximations.
On conjectures of Minkowski and Woods for n=8
On consecutive integers of the form ax², by² and cz²
On continued fractions and diophantine approximation in power series fields
On Continued Fractions and Finite Automata.
On cubic Thue inequalities and a result of Mahler
On density modulo 1 of some expressions containing algebraic integers
On Dirichlet's theorem concerning diophantine approximation
On Dispersion and Markov Constants.
On Dyson's lemma
On effective measures of irrationality for ... and related numbers.
On Ergodic Theory of A. Schmidt's Complex Continued Fractions over Gaussian Field.
On families of Pisot -sequences
On gaps in Rényi -expansions of unity for an algebraic number
Let be an algebraic number. We study the strings of zeros (“gaps”) in the Rényi -expansion of unity which controls the set of -integers. Using a version of Liouville’s inequality which extends Mahler’s and Güting’s approximation theorems, the strings of zeros in are shown to exhibit a “gappiness” asymptotically bounded above by , where is the Mahler measure of . The proof of this result provides in a natural way a new classification of algebraic numbers with classes called Q...
On generalised arithmetic and geometric progressions
On heights of multiplicatively dependent algebraic numbers