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BOUNDED PARTIAL QUOTIENTS OF SOME CUBIC POWER SERIES WITH BINARY COEFFICIENTS
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 Title & Authors
BOUNDED PARTIAL QUOTIENTS OF SOME CUBIC POWER SERIES WITH BINARY COEFFICIENTS
Ayadi, Khalil; Beldi, Salah; Lee, Kwankyu;
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 Abstract
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.
 Keywords
power series;continued fraction;finite fields;
 Language
English
 Cited by
 References
1.
L. E. Baum and M. M. Sweet, Continued fractions of algebraic power series in characteristic 2, Ann. of Math. (2) 103 (1976), no. 3, 593-610. crossref(new window)

2.
B. de Mathan, Approximation exponents for algebraic functions in positive characteristic, Acta Arith. 60 (1992), no. 4, 359-370. crossref(new window)

3.
D. Gomez-Perez and A. Lasjaunias, Hyperquadratic power series in $F_{3}((T^{-1}))$ with partial quotients of degree 1, Ramanujan J. 33 (2014), no. 2, 219-226. crossref(new window)

4.
A. I. Khinchin, Continued Fractions, University of Chicago Press, 1964.

5.
A. Lasjaunias, Continued fractions for algebraic formal power series over a finite base field, Finite Fields Appl. 5 (1999), no. 1, 46-56. crossref(new window)

6.
A. Lasjaunias, Quartic power series in $F_{3}((T^{-1}))$ with bounded partial quotients, Acta Arith. 95 (2000), no. 1, 49-59. crossref(new window)

7.
A. Lasjaunias and J.-J. Ruch, Algebraic and badly approximable power series over a finite field, Finite Fields Appl. 8 (2002), no. 1, 91-107. crossref(new window)

8.
A. Lasjaunias and J.-J. Ruch, Flat power series over a finite field, J. Number Theory 95 (2002), no. 2, 268-288. crossref(new window)

9.
A. Lasjaunias and J.-Y. Yao, Hyperquadratic continued fractions in odd characteristic with partial quotients of degree one, J. Number Theory 149 (2015), 259-284. crossref(new window)

10.
K. Lee, Continued fractions for linear fractional transformations of power series, Finite Fields Appl. 11 (2005), no. 1, 45-55. crossref(new window)

11.
W. H. Mills and D. P. Robbins, Continued fractions for certain algebraic power series, J. Number Theory 23 (1986), no. 3, 388-404. crossref(new window)

12.
M. Mkaouar, Sur les fractions continues des series formelles quadratiques sur $f_q(x)$, Acta Arith. 97 (2001), no. 3, 241-251. crossref(new window)

13.
W. M. Schmidt, On continued fractions and diophantine approximation in power series fields, Acta Arith. 95 (2000), no. 2, 139-166. crossref(new window)

14.
D. S. Thakur, Diophantine approximation exponents and continued fractions for algebraic power series, J. Number Theory 79 (1999), no. 2, 284-291. crossref(new window)

15.
J. F. Voloch, Diophantine approximation in positive characteristic, Period. Math. Hungar. 19 (1988), no. 3, 217-225. crossref(new window)