On the Distribution of Sequences Connected with Good Lattice Points.
On the frequency of small fractional parts in certain real sequences, IV
On the gaps of the Lagrange spectrum
On the Gaps of the Markoff Spectrum.
On the invariant measure for Jacobi-Perron algorithm.
On the Khintchine constant for centred continued fraction expansions.
On the length of the continued fraction for values of quotients of power sums
Generalizing a result of Pourchet, we show that, if are power sums over satisfying suitable necessary assumptions, the length of the continued fraction for tends to infinity as . This will be derived from a uniform Thue-type inequality for the rational approximations to the rational numbers , .
On the Lower Markov Spectrum.
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 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 powers of Motzkin paths.
On the Ramanujan AGM fraction. II: The complex-parameter case.
On the random character of fundamental constant expansions.
On the sums of continued fractions
On the theorem of Gauss-Kusmin-Lévy and a Frobenius-type theorem for function spaces
On the Transcendence and Algebraic Independence of Certain Continued Fractions.
On two theorems of Kopetzky and Schnitzer on the approximation of continued fractions.
p-adische Kettenbrüche und Irrationalität p-adischer Zahlen.
Palindromic continued fractions
In the present work, we investigate real numbers whose sequence of partial quotients enjoys some combinatorial properties involving the notion of palindrome. We provide three new transendence criteria, that apply to a broad class of continued fraction expansions, including expansions with unbounded partial quotients. Their proofs heavily depend on the Schmidt Subspace Theorem.