A Best Lower Bound for Good Lattice Points.
A bound for the discrepancy of digital nets and its application to the analysis of certain pseudo-random number generators
A combinatorial method for construction normal numbers.
A comparison of dispersion and Markov constants
A conjecture of Erdös on continued fractions
A conjecture of Kátai
A construction of low-discrepancy sequences using global function fields
A construction of pseudorandom binary sequences using both additive and multiplicative characters
A generalization of the Davenport-Erdős construction of normal numbers
We extend the Davenport and Erdős construction of normal numbers to the case.
A Direct Proof of a Theorem of Roth.
A dual approach to triangle sequences: a multidimensional continued fraction algorithm.
A family of pseudorandom binary sequences constructed by the multiplicative inverse
A fibered system associated with the prime number sequence. (Sur un système fibré lié à la suite des nombres premiers.)
A further discussion of the Hausdorff dimension in Engel expansions
A Gauss-Kuzmin theorem for the Rosen fractions
Using the natural extensions for the Rosen maps, we give an infinite-order-chain representation of the sequence of the incomplete quotients of the Rosen fractions. Together with the ergodic behaviour of a certain homogeneous random system with complete connections, this allows us to solve a variant of Gauss-Kuzmin problem for the above fraction expansion.
A Gauss-Kuzmin-Lévy theorem for a certain continued fraction.
A general arithmetic construction of transcendental non-Liouville normal numbers from rational fractions
A general discrepancy estimate based on p-adic arithmetics
A general notion of independence of sequences of integers.
A generalization of a theorem of Erdős-Rényi to m-fold sums and differences
Let m ≥ 2 be a positive integer. Given a set E(ω) ⊆ ℕ we define to be the number of ways to represent N ∈ ℤ as a combination of sums and differences of m distinct elements of E(ω). In this paper, we prove the existence of a “thick” set E(ω) and a positive constant K such that for all N ∈ ℤ. This is a generalization of a known theorem by Erdős and Rényi. We also apply our results to harmonic analysis, where we prove the existence of certain thin sets.