Add to ORKGAbstract. In this paper, we give a new proof of a result due to Bézivin that a D-finite Mahler function is necessarily rational. This also gives a new proof of the rational–transcendental dichotomy of Mahler functions due to Nishioka. Using our method of proof, we also provide a new proof of a Pólya–Carlson type result for Mahler functions due to Randé; that is, a Mahler function which is meromorphic in the unit disk is either rational or has the unit circle as a natural boundary. 1
97 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1983.The Skolem-Mahler-Lech theorem...
International audienceThe guiding thread of the present work is the following result, in the vain of...
It is a classical result of Mahler that for any rational number α > 1 which is not an integer and an...
In this paper, we give a new proof of a result due to Bèzivin that a D-finite Mahler function is nec...
We construct Mahler discrete residues for rational functions and show that they comprise a complete ...
International audienceLet K be a function field of characteristic p > 0. We recently established the...
52 pagesLet $K$ be a field of characteristic zero and $k$ and $l$ be two multiplicatively independen...
This thesis is part of Number Theory. It deals with transcendence and algebraic independence of valu...
AbstractIn the vein of Christol, Kamae, Mendès France and Rauzy, we consider the analogue of a probl...
Recently we constructed Mahler discrete residues for rational functions and showed they comprise a c...
We consider some lacunary power series with rational coefficients in Q(p). We show that under certai...
In this thesis, we investigate topics belonging to number theory, and especially to transcendental n...
Suppose that F (x) ∈ Z[[x]] is a Mahler function and that 1/b is in the radius of convergence of F ...
Suppose that F(x) ∈ ℤ[x] is a Mahler function and that 1/b is in the radius of convergence of F(x) f...
International audienceIn 1990, Ku. Nishioka proved a fundamental theorem for Mahler's method, which ...
97 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1983.The Skolem-Mahler-Lech theorem...
International audienceThe guiding thread of the present work is the following result, in the vain of...
It is a classical result of Mahler that for any rational number α > 1 which is not an integer and an...
In this paper, we give a new proof of a result due to Bèzivin that a D-finite Mahler function is nec...
We construct Mahler discrete residues for rational functions and show that they comprise a complete ...
International audienceLet K be a function field of characteristic p > 0. We recently established the...
52 pagesLet $K$ be a field of characteristic zero and $k$ and $l$ be two multiplicatively independen...
This thesis is part of Number Theory. It deals with transcendence and algebraic independence of valu...
AbstractIn the vein of Christol, Kamae, Mendès France and Rauzy, we consider the analogue of a probl...
Recently we constructed Mahler discrete residues for rational functions and showed they comprise a c...
We consider some lacunary power series with rational coefficients in Q(p). We show that under certai...
In this thesis, we investigate topics belonging to number theory, and especially to transcendental n...
Suppose that F (x) ∈ Z[[x]] is a Mahler function and that 1/b is in the radius of convergence of F ...
Suppose that F(x) ∈ ℤ[x] is a Mahler function and that 1/b is in the radius of convergence of F(x) f...
International audienceIn 1990, Ku. Nishioka proved a fundamental theorem for Mahler's method, which ...
97 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1983.The Skolem-Mahler-Lech theorem...
International audienceThe guiding thread of the present work is the following result, in the vain of...
It is a classical result of Mahler that for any rational number α > 1 which is not an integer and an...