On the approximability of the logarithms of algebraic numbers
On the binary expansions of algebraic numbers
Employing concepts from additive number theory, together with results on binary evaluations and partial series, we establish bounds on the density of 1’s in the binary expansions of real algebraic numbers. A central result is that if a real has algebraic degree , then the number of 1-bits in the expansion of through bit position satisfiesfor a positive number (depending on ) and sufficiently large . This in itself establishes the transcendency of a class of reals where the integer-valued...
On the distribution of the sequence (nα) with transcendental α
On the Gelfond-Feldman measure of algebraic independence
On the greatest prime factor of
On the greatest prime factors of polynomials at integer points
On the Oesterlé-Masser Conjecture.
On the order function of a transcendental number
On the orders of zero of certain functions
On the Possibility of Finding Certain Criteria for the Irrationality of a Number Defined as a Limit of a Sequence of Rational Numbers.
On the quasi-periodic -adic Ruban continued fractions
We study a family of quasi periodic -adic Ruban continued fractions in the -adic field and we give a criterion of a quadratic or transcendental -adic number which based on the -adic version of the subspace theorem due to Schlickewei.
On the simultaneous approximation of , and
On the simultaneous approximation of certain numbers.
On the simultaneous diophantine approximation of values of certain hypergeometric and algebraic functions
ON the transcendence and algebraic independence of certain somewhat amusing numbers (results of Loxton and van der Poorten).
On the transcendence of certain power series of algebraic numbers
On the uniform ε-distribution of residues within the periods of rational fractions with applications to normal numbers
On the values of a class of analytic functions at algebraic points