arXiv subjects

Ali Kacha

Publications and source records attributed to Ali Kacha.

5 recordsLinked to original sources

arXiv2026

On algebraic independence of three p-adic continued fractions

In this paper, we establish sufficient conditions on the elements of the p-adic continued fractions $A$ and $B$ which guarantee that the p-adic continued fractions $A, B $ and $A^{B}$ are algebraically independent over $\mathbb{Q}$. These elements have partial quotients that increase rapidly. We note that these results extend some work of Bundschuh. Furthermore, we give some numerical examples which illustrated the theoretical results.

math.NT↗

arXiv2024

On the transcendence of some operations of infinite series

In the present paper and as an application of Roth's theorem concerning the rational approximation of algebraic numbers, we give a sufficient condition that will assure us that a sum, product and quotient of some series of positive rational terms are transcendental numbers. We recall that all the infinite series that we are going to treat are Liouville numbers. At the end this article, we establish an approximation measure of these numbers.

math.NT↗

arXiv2023

Transcendence of some infinite series

In the present paper and as an application of Roth's theorem concerning the rational approximation of algebraic numbers, we give a sufficient condition that will assure us that a series of positive rational terms is a transcendental number. With the same conditions, we establish a transcendental measure of $ \sum_{n = 1}^{\infty} 1/a_n$.

math.NT↗

arXiv2022

Transcendental Continued Fractions

In the present paper, we give sufficient conditions on the elements of the continued fractions $A$ and $B$ that will assure us that the continued fraction $A^B$ is a transcendental number. With the same condition, we establish a transcendental measure of $A^B.$

math.NT↗

arXiv2022

Continued fraction representations of the generalized operator entropy

The direct calculation of the Generalized operator entropy proves difficult by the appearance of rational exponents of matrices. The main motivation of this work is to overcome these difficulties and to present a practical and efficient method for this calculation using its representation by the matrix continued fraction. At the end of our paper, we deduce a continued fraction expansion of the Bregman operator divergence. Some numerical examples illutrating the theoretical result are discussed.

math.NA↗