On the linear independence of the values of Gauss hypergeometric function
On the Lower Markov Spectrum.
On the Maximal Length of Two Sequences of Integers in Arithmetic Progressions with the Same Prime Divisors.
On the metric theory of inhomogeneous diophantine approximations
On the multiples of a badly approximable vector
Let d be a positive integer and α a real algebraic number of degree d + 1. Set . It is well-known that , where ||·|| denotes the distance to the nearest integer. Furthermore, for any integer n ≥ 1. Our main result asserts that there exists a real number C, depending only on α, such that for any integer n ≥ 1.
On the (non-)existence of m-cycles for generalized Syracuse sequences
On the non-quadraticity of values of the q-exponential function and related q-series
On the number of good approximations of algebraic numbers by algebraic numbers of bounded degree
On the number of solutions of simultaneous Pell equations II
On the Oesterlé-Masser Conjecture.
On the order function of a transcendental number
On the orders of zero of certain functions
On the problem
On the period length of some special continued fractions
We investigate and refine a device which we introduced in [3] for the study of continued fractions. This allows us to more easily compute the period lengths of certain continued fractions and it can be used to suggest some aspects of the cycle structure (see [1]) within the period of certain continued fractions related to underlying real quadratic fields.
On the period of the continued fraction for values of the square root of power sums
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 power values of Stirling numbers
On the powers of Motzkin paths.
On the quantitative unit sum number problem-an application of the subspace theorem
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.