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math.NT2026
On algebraic independence of three p-adic continued fractions
Sarra Ahallal, Mohamed Begare, Ali Kacha
In this paper, we establish sufficient conditions on the elements of the p-adic continued fractions and which guarantee that the p-adic continued fractions and $A^{…
math.NT2024
On the transcendence of some operations of infinite series
Sarra Ahallal, Fedoua Sghiouer, Ali Kacha
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 s…