On a quantitative refinement of the Lagrange spectrum
On a quantitative version of the Oppenheim conjecture.
On a question of S. Chowla
On a question of Schmidt and Summerer concerning -systems
Following a suggestion of W.M. Schmidt and L. Summerer, we construct a proper -system with the property . In fact, our method generalizes to provide -systems with , for arbitrary . We visualize our constructions with graphics. We further present explicit examples of numbers that induce the -systems in question.
On a question regarding visibility of lattice points, II
On a question related to diophantine approximation
On a result of Mahler on the decimal expansions of (nα)
On a simultaneous approximation problem concerning binary recurrences.
On a theorem of Legendre in the theory of continued fractions
On a theorem of Ramachandra
On a Theorem of S. Sivasankaranarayana Pillai
On a theorem of Segre
On a theorem of V. Bernik in the metric theory of Diophantine approximation
On absolute (j, ε)-normality in the rational fractions with applications to normal numbers
On an equation of Goormaghtigh
On an estimate for the orders of zeros of Mahler type functions
On an extension of a theorem of S. Chowla
On an extension of Euler numbers and records of alternating permutations. (Sur une extension des nombres d'Euler et les records des permutations alternantes.)
On approximation by Lüroth series
Let and be its sequence of Lüroth Series convergents. Define the approximation coefficients by . In [BBDK] the limiting distribution of the sequence was obtained for a.e. using the natural extension of the ergodic system underlying the Lüroth Series expansion. Here we show that this can be done without the natural extension. In fact we will prove that for each is already distributed according to the limiting distribution. Using the natural extension we will study the distribution for...
On approximation of real numbers by real algebraic numbers