Hausdorff dimension, lower order and Khintchine's theorem in metric Diophantine approximation.
Inhomogeneous Diophantine approximation on integer polynomials with non-monotonic error function
We prove that the Lebesgue measure of the set of real points which are inhomogeneously Ψ-approximable by polynomials, where Ψ is not necessarily monotonic, is zero.
Khinchin's theorem in k dimensions with prime numerator and denominator
La répartition modulo de la suite et les ensembles de Cantor
Lower bounds for the number of integral polynomials with given order of discriminants
Meilleures approximations diophantiennes d’un élément du tore
Metric Diophantine approximation on the middle-third Cantor set
Let be a real number and let denote the set of real numbers approximable at order at least by rational numbers. More than eighty years ago, Jarník and, independently, Besicovitch established that the Hausdorff dimension of is equal to . We investigate the size of the intersection of with Ahlfors regular compact subsets of the interval . In particular, we propose a conjecture for the exact value of the dimension of intersected with the middle-third Cantor set and give several results...
Metric inhomogeneous Diophantine approximation on the field of formal Laurent series
Metric results on the approximation of zero by linear combinations of independent and of dependent rationals.
Metrical results on sums of squares and prime values of the integer parts of sequences
Metrical theorems for inhomogeneous Diophantine approximation in positive characteristic
Metrische Sätze über simultane Approximation abhängiger Größen.
Multiplicative zero-one laws and metric number theory
We develop the classical theory of Diophantine approximation without assuming monotonicity or convexity. A complete 'multiplicative' zero-one law is established akin to the 'simultaneous' zero-one laws of Cassels and Gallagher. As a consequence we are able to establish the analogue of the Duffin-Schaeffer theorem within the multiplicative setup. The key ingredient is the rather simple but nevertheless versatile 'cross fibering principle'. In a nutshell it enables us to 'lift' zero-one laws to higher...
Non-Typical Points for β-Shifts
We study sets of non-typical points under the map mod 1 for non-integer β and extend our results from [Fund. Math. 209 (2010)] in several directions. In particular, we prove that sets of points whose forward orbit avoid certain Cantor sets, and the set of points for which ergodic averages diverge, have large intersection properties. We observe that the technical condition β > 1.541 found in the above paper can be removed.
Note on the density constant in the distribution of self-numbers. II
Dimostriamo che la costante che regola la distribuzione dei cosiddetti self numbers è un numero trascendente. Ciò precisa un risultato dimostrato in un precedente articolo dal medesimo titolo, ossia che tale costante sia irrazionale. Il metodo fa uso di una curiosa formula per l'espansione 2-adica di tale numero (già utilizzata nell'altro lavoro) e del profondo Teorema del Sottospazio.
On a measure theoretic aspect of diophantine approximation.
On a metrical theorem of W. Schmidt
On a theorem of V. Bernik in the metric theory of Diophantine approximation
On approximation of real numbers by real algebraic numbers
On Baker type lower bounds for linear forms
A criterion is given for studying (explicit) Baker type lower bounds of linear forms in numbers over the ring of an imaginary quadratic field . This work deals with the simultaneous auxiliary functions case.