Add to ORKGLet {a_{1}(n)}_{n>1} be a purely periodic sequence of nonnegative integers, not identically zero, and {a_{ell}(n)}_{ngeq 1}overline{(}ell=2, 3, ldots) be the sequences defined inductively by a_{ell}(n):=displaystyle sum_{d|n}a_{ell-1}(d). Then, for an arbitrary integer q(|q|>1), the numbers 1 and displaystyle sum{n=1}^{infty}a{l}(n)q (ell=2, 3, ldots) are linearly independent over mathbb{Q}. In particular, the numbers 1 and displaystyle sum{n=1}^{infty}d{el}(n)q^{-n}(ell=2, 3, . are linearly independent over mathbb{Q}, where d_{ell}(n) are generalized divisor functions
summary:Let $\mathbb {N}$ be the set of positive integers and let $s\in \mathbb {N}$. We denote by $...
AbstractWe prove Q-linear independence results for the values of the q-seriesTqt(z)=∑ν=0∞q−tν(ν+1)/2...
The paper deals with the so-called linearly unrelated se-quences. The criterion and the application ...
Let sigma(k)(n) denote the sum of the k-th powers of the positive divisors of n. Erdos and Kac conje...
In this note we investigate arithmetic properties of values of the Tschakaloff function Tq(z) = Σ<su...
AbstractLet σk(n) denote the sum of the k-th powers of the positive divisors of n. Erdős and Kac con...
Let $(i,j)\in \mathbb{N}\times \mathbb{N}_{\geq2}$ and $S_{i,j}$ be an infinite subset of positive i...
In this paper, we give a new criterion for the algebraic independence of the values of power series....
AbstractThe main theorem of this paper, proved using Mahler's method, gives a necessary and sufficie...
We give certain optimal inequalities for the divisor function. Such inequalities are useful in estim...
Abstract: A criterion for linear independence, similar to that established in 2002 by Hančl in the ...
We consider a $G$-function $F(z)=\sum_{k=0}^{\infty} A_k z^k \in \mathbb{K}[[z]]$, where $\mathbb{K}...
AbstractLet σj(n)=∑d|ndj be the sum of divisors function, and let I be the identity function. When c...
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...
summary:Let $\mathbb {N}$ be the set of positive integers and let $s\in \mathbb {N}$. We denote by $...
AbstractWe prove Q-linear independence results for the values of the q-seriesTqt(z)=∑ν=0∞q−tν(ν+1)/2...
The paper deals with the so-called linearly unrelated se-quences. The criterion and the application ...
Let sigma(k)(n) denote the sum of the k-th powers of the positive divisors of n. Erdos and Kac conje...
In this note we investigate arithmetic properties of values of the Tschakaloff function Tq(z) = Σ<su...
AbstractLet σk(n) denote the sum of the k-th powers of the positive divisors of n. Erdős and Kac con...
Let $(i,j)\in \mathbb{N}\times \mathbb{N}_{\geq2}$ and $S_{i,j}$ be an infinite subset of positive i...
In this paper, we give a new criterion for the algebraic independence of the values of power series....
AbstractThe main theorem of this paper, proved using Mahler's method, gives a necessary and sufficie...
We give certain optimal inequalities for the divisor function. Such inequalities are useful in estim...
Abstract: A criterion for linear independence, similar to that established in 2002 by Hančl in the ...
We consider a $G$-function $F(z)=\sum_{k=0}^{\infty} A_k z^k \in \mathbb{K}[[z]]$, where $\mathbb{K}...
AbstractLet σj(n)=∑d|ndj be the sum of divisors function, and let I be the identity function. When c...
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...
summary:Let $\mathbb {N}$ be the set of positive integers and let $s\in \mathbb {N}$. We denote by $...
AbstractWe prove Q-linear independence results for the values of the q-seriesTqt(z)=∑ν=0∞q−tν(ν+1)/2...
The paper deals with the so-called linearly unrelated se-quences. The criterion and the application ...