13 citations · 42 across the 14 of their papers we have counts for
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Transcendence and continued fraction expansion of values of Hecke-Mahler series
Yann Bugeaud, Michel Laurent
Let and be real numbers with and irrational. We show that the Hecke-Mahler series $$ F_{θ, ρ} (z_1, z_2) = \sum_{k_1 \ge 1} \, \sum_{k_2 = 1}^{\lfloor k…
Combinatorial structure of Sturmian words and continued fraction expansions of Sturmian numbers
Yann Bugeaud, Michel Laurent
Let be the continued fraction expansion of an irrational real number . It is well-known that the characteristic Sturmian word of slope is…
On the Diophantine nature of the elements of Cantor sets arising in the dynamics of contracted rotations
Yann Bugeaud, Dong Han Kim, Michel Laurent +1
We prove that these Cantor sets are made up of transcendental numbers, apart from their endpoints and , under some arithmetical assumptions on the data. To that purpose, we…
On Kronecker's density theorem, primitive points and orbits of matrices
Michel Laurent
We discuss recent quantitative results in connexion with Kronecker's theorem on the density of subgroups in R^n and with Dani and Raghavan's theorem on the density of orbits in the…
Multi-dimensional metric approximation by primitive points
S. G. Dani, Michel Laurent, Arnaldo Nogueira
We refine metrical statements in the style of the Khintchine-Groshev Theorem by requiring certain coprimality constraints on the coordinates of the integer solutions.
Inhomogeneous approximation with coprime integers and lattice orbits
Michel Laurent, Arnaldo Nogueira
We obtain variants of the classical Minkowski Theorem on inhomogeneous approximation where we require moreover that the solutions be coprime integers. We link the subject wi…