AbstractLet σk(n) denote the sum of the k-th powers of the positive divisors of n. Erdős and Kac conjectured that the sumαk=∑n=1∞σk(n)n! is irrational for k⩾1. This is known to be true for k=1, 2 and 3. Fix r⩾1. In this article we give a precise criterion for 1,α1,…,αr to be Q-linearly independent, assuming a standard conjecture of Schinzel on the prime values taken by a family of polynomials. We have verified our criterion for r=50
The thesis deals with the irrationality, irrational sequences, linearly independent sums of series a...
AbstractCarlitz defined both a function ζ and a formal power series Π over Fq, analogous to the Riem...
AbstractWe prove that the number τ=∑l=0∞dl/∏j=1l(1+djr+d2js), where d∈Z, |d|>1, and r,s∈Q, s≠0, are ...
Let sigma(k)(n) denote the sum of the k-th powers of the positive divisors of n. Erdos and Kac conje...
For positive integers $k$ and $n$ let $\sigma_k(n)$ denote the sum of the $k$th powers of the diviso...
Denote by sigma(k)(n) the sum of the k-th powers of the divisors of n, and let S-k = Sigma(n >= 1) (...
Here, we show, unconditionally for k = 3, and on the prime k-tuples conjecture for k ≥ 4, that n=1 σ...
Let {a_{1}(n)}_{n>1} be a purely periodic sequence of nonnegative integers, not identically zero, an...
This Ph.D. thesis lies in the path opened by Apéry who proved the irrationality of ζ(3) andalready f...
We prove sharp irrationality measures for a q-analogue of π and related q-series, and indicate open ...
(To our friend Keijo Väänänen on the occasion of his sixtieth birthday) We prove sharp irrationality...
AbstractLet ξ be a real irrational number, and φ be a function (satisfying some assumptions). In thi...
AbstractIn this paper we derive some irrationality and linear independence results for series of the...
AbstractThe function f(θ, φ; x, y) = Σk = 1∞ Σ1 ≤ m ≤ kθ + φ xkym, where θ > 0 is irrational and φ i...
In this masters thesis we prove by contradiction the irrationality of the numbers e, π 2 , and √n m,...
The thesis deals with the irrationality, irrational sequences, linearly independent sums of series a...
AbstractCarlitz defined both a function ζ and a formal power series Π over Fq, analogous to the Riem...
AbstractWe prove that the number τ=∑l=0∞dl/∏j=1l(1+djr+d2js), where d∈Z, |d|>1, and r,s∈Q, s≠0, are ...
Let sigma(k)(n) denote the sum of the k-th powers of the positive divisors of n. Erdos and Kac conje...
For positive integers $k$ and $n$ let $\sigma_k(n)$ denote the sum of the $k$th powers of the diviso...
Denote by sigma(k)(n) the sum of the k-th powers of the divisors of n, and let S-k = Sigma(n >= 1) (...
Here, we show, unconditionally for k = 3, and on the prime k-tuples conjecture for k ≥ 4, that n=1 σ...
Let {a_{1}(n)}_{n>1} be a purely periodic sequence of nonnegative integers, not identically zero, an...
This Ph.D. thesis lies in the path opened by Apéry who proved the irrationality of ζ(3) andalready f...
We prove sharp irrationality measures for a q-analogue of π and related q-series, and indicate open ...
(To our friend Keijo Väänänen on the occasion of his sixtieth birthday) We prove sharp irrationality...
AbstractLet ξ be a real irrational number, and φ be a function (satisfying some assumptions). In thi...
AbstractIn this paper we derive some irrationality and linear independence results for series of the...
AbstractThe function f(θ, φ; x, y) = Σk = 1∞ Σ1 ≤ m ≤ kθ + φ xkym, where θ > 0 is irrational and φ i...
In this masters thesis we prove by contradiction the irrationality of the numbers e, π 2 , and √n m,...
The thesis deals with the irrationality, irrational sequences, linearly independent sums of series a...
AbstractCarlitz defined both a function ζ and a formal power series Π over Fq, analogous to the Riem...
AbstractWe prove that the number τ=∑l=0∞dl/∏j=1l(1+djr+d2js), where d∈Z, |d|>1, and r,s∈Q, s≠0, are ...
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