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CONTINUED FRACTION AND DIOPHANTINE EQUATION
Gadri, Wiem,Mkaouar, Mohamed Korean Mathematical Society 2016 대한수학회보 Vol.53 No.3
Our paper is devoted to the study of certain diophantine equations on the ring of polynomials over a finite field, which are intimately related to algebraic formal power series which have partial quotients of unbounded degree in their continued fraction expansion. In particular it is shown that there are Pisot formal power series with degree greater than 2, having infinitely many large partial quotients in their simple continued fraction expansions. This generalizes an earlier result of Baum and Sweet for algebraic formal power series.
Continued fraction and Diophantine equation
Wiem Gadri,Mohamed Mkaouar 대한수학회 2016 대한수학회보 Vol.53 No.3
Our paper is devoted to the study of certain diophantine equations on the ring of polynomials over a finite field, which are intimately related to algebraic formal power series which have partial quotients of unbounded degree in their continued fraction expansion. In particular it is shown that there are Pisot formal power series with degree greater than 2, having infinitely many large partial quotients in their simple continued fraction expansions. This generalizes an earlier result of Baum and Sweet for algebraic formal power series.
ON PERIODIC P-CONTINUED FRACTION HAVING PERIOD LENGTH ONE
Chandoul, Amara,Amar, Hela Ben,Mkaouar, Mohamed Korean Mathematical Society 2013 대한수학회보 Vol.50 No.5
The aim of this paper is to prove that every quadratic formal power series ${\omega}$ can be expressed as a periodic non-simple continued fraction having period length one.
ON PERIODIC P-CONTINUED FRACTION HAVING PERIOD LENGTH ONE
Amara Chandoul,Hela Ben Amar,Mohamed Mkaouar 대한수학회 2013 대한수학회보 Vol.50 No.5
The aim of this paper is to prove that every quadratic for- mal power series ω can be expressed as a periodic non-simple continued fraction having period length one.