Intermediate Diophantine exponents and parametric geometry of numbers
Khintchine-type theorems on manifolds
Linear forms of a given Diophantine type
We prove a result on the existence of linear forms of a given Diophantine type.
Linear polynomials in numbers of bounded degree
Lower bounds for simultaneous Diophantine approximation constants
After a brief exposition of the state-of-art of research on the (Euclidean) simultaneous Diophantine approximation constants , new lower bounds are deduced for and .
Meilleures approximations diophantiennes d’un élément du tore
Meilleures approximations diophantiennes simultanées et théorème de Lévy
D'après le théorème de Lévy, les dénominateurs du développement en fraction continue d'un réel croissent presque sûrement à une vitesse au plus exponentielle. Nous étendons cette estimation aux meilleures approximations diophantiennes simultanées de formes linéaires.
Meilleures approximations d'un élément du tore 𝕋² et géométrie de la suite des multiples de cet élément
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...
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 mixed Littlewood conjecture for quadratic numbers
We study a simultaneous diophantine problem related to Littlewood’s conjecture. Using known estimates for linear forms in -adic logarithms, we prove that a previous result, concerning the particular case of quadratic numbers, is close to be the best possible.
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 simultaneous approximation problem concerning binary recurrences.
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.
On commuting circle mappings and simultaneous Diophantine approximations.