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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.
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참고문헌 (19)
참고문헌 신청
Y. Amice / Les nombres p-adiques / PUF Collection Sup
P. Bateman / 1962 / The analogue of the Pisot-Vijayaraghavan numbers in fields of formal power series / Illinois J. Math 6:594~606
L. E. Baum / 1976 / Continued fraction of algebraic power series in charac-teristic 2 / Ann. of Math 103(3):593~610
M. J. Bertin / 1992 / Pisot and Salem Numbers / Birkhauser Verlag Basel
H. Davenport / 1964 / A remark on continued fractions / Michigan Math. J 11:343~344
P. Bateman / 1962 / The analogue of the Pisot-Vijayaraghavan numbers in fields of formal power series / Illinois J. Math 6:594~606
L. E. Baum / 1976 / Continued fraction of algebraic power series in charac-teristic 2 / Ann. of Math 103(3):593~610
M. J. Bertin / 1992 / Pisot and Salem Numbers / Birkhauser Verlag Basel
H. Davenport / 1964 / A remark on continued fractions / Michigan Math. J 11:343~344
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