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It is a surprising but now well-known fact that there exist algebraic power series of degree higher than two with partial quotients of bounded degrees in their continued fraction expansions, while there is no single algebraic real number known with bounded partial quotients. However, it seems that these special algebraic power series are quite rare and it is hard to determine their continued fraction expansions explicitly. To the short list of known examples, we add a new family of cubic power series with bounded partial quotients.
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참고문헌 (15)
참고문헌 신청
L. E. Baum / 1976 / Continued fractions of algebraic power series in charac-teristic 2 / Ann. of Math. (2) 103(3):593~610
B. de Mathan / 1992 / Approximation exponents for algebraic functions in positive character-istic / Acta Arith 60(4):359~370
D. Gomez-Perez / 2014 / Hyperquadratic power series in F3((T−1)) with partial quotients of degree 1 / Ramanujan J 33(2):219~226
A. I. Khinchin / 1964 / Continued Fractions / University of Chicago Press
A. Lasjaunias / 1999 / Continued fractions for algebraic formal power series over a finite base field / Finite Fields Appl 5(1):46~56
B. de Mathan / 1992 / Approximation exponents for algebraic functions in positive character-istic / Acta Arith 60(4):359~370
D. Gomez-Perez / 2014 / Hyperquadratic power series in F3((T−1)) with partial quotients of degree 1 / Ramanujan J 33(2):219~226
A. I. Khinchin / 1964 / Continued Fractions / University of Chicago Press
A. Lasjaunias / 1999 / Continued fractions for algebraic formal power series over a finite base field / Finite Fields Appl 5(1):46~56
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