Add to ORKGIn this paper, we give a new criterion for the algebraic independence of the values of power series. In particular, we deduce the algebraic independence of the values displaystyle sum_{m=0}^{infty}$beta$^{-w_{m}}, where $beta$ is a Pisot or Salem number and (w_{m})_{rn=0}^{infty} is a certain increasing sequence of nonnegative integers satisfying mathrm{h}mathrm{m}_{mrightarrowinfty}w_{m+1}/w_{m}=1
AbstractThe formal power series[formula]is transcendental over Q(X) whentis an integer ≥2. This is d...
This article investigates an efficient way of evaluating sums and series, based on a result of Abel ...
The theory of arithmetic functions and the theory of formal power series are classical and active pa...
International audienceUsing Borwein's simple analytic method for the irrationality of the $q$-logari...
AbstractLet q⩾2 be an integer and let w be a block of 0, …, q−1 of finite length. For a nonnegative ...
Let {a_{1}(n)}_{n>1} be a purely periodic sequence of nonnegative integers, not identically zero, an...
We deepen here the insight on formal power series. We temporarily abandon formality and consider the...
International audienceIn this paper, the algebraic independence of values of the functionG d (z) := ...
AbstractThe function f(θ, φ; x, y) = Σk = 1∞ Σ1 ≤ m ≤ kθ + φ xkym, where θ > 0 is irrational and φ i...
For a certain class of power series, infinite products, and Lambert type series, we establish a nece...
Algebraic independence of power series generated by linearly independent positive numbers b
AbstractThe main theorem of this paper, proved using Mahler's method, gives a necessary and sufficie...
Given any non-polynomial $G$-function $F(z)=\sum_{k=0}^\infty A_k z^k$ of radius of convergence $R$,...
A lacunary series is a Taylor series with large gaps between its non-zero coefficients. In this thes...
This paper concerns power series of an arithmetic nature that arise in the analysis of divide-and-co...
AbstractThe formal power series[formula]is transcendental over Q(X) whentis an integer ≥2. This is d...
This article investigates an efficient way of evaluating sums and series, based on a result of Abel ...
The theory of arithmetic functions and the theory of formal power series are classical and active pa...
International audienceUsing Borwein's simple analytic method for the irrationality of the $q$-logari...
AbstractLet q⩾2 be an integer and let w be a block of 0, …, q−1 of finite length. For a nonnegative ...
Let {a_{1}(n)}_{n>1} be a purely periodic sequence of nonnegative integers, not identically zero, an...
We deepen here the insight on formal power series. We temporarily abandon formality and consider the...
International audienceIn this paper, the algebraic independence of values of the functionG d (z) := ...
AbstractThe function f(θ, φ; x, y) = Σk = 1∞ Σ1 ≤ m ≤ kθ + φ xkym, where θ > 0 is irrational and φ i...
For a certain class of power series, infinite products, and Lambert type series, we establish a nece...
Algebraic independence of power series generated by linearly independent positive numbers b
AbstractThe main theorem of this paper, proved using Mahler's method, gives a necessary and sufficie...
Given any non-polynomial $G$-function $F(z)=\sum_{k=0}^\infty A_k z^k$ of radius of convergence $R$,...
A lacunary series is a Taylor series with large gaps between its non-zero coefficients. In this thes...
This paper concerns power series of an arithmetic nature that arise in the analysis of divide-and-co...
AbstractThe formal power series[formula]is transcendental over Q(X) whentis an integer ≥2. This is d...
This article investigates an efficient way of evaluating sums and series, based on a result of Abel ...
The theory of arithmetic functions and the theory of formal power series are classical and active pa...