DOI QR코드

DOI QR Code

ON PERIODIC P-CONTINUED FRACTION HAVING PERIOD LENGTH ONE

  • Received : 2012.09.23
  • Published : 2013.09.30

Abstract

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.

References

  1. E. B. Burger, J. Gell-Redman, R. Kravitz, D. Walton, and N. Yates, Shrinking the period lengths of continued fractions while still capturing convergents, J. Number Theory 128 (2008), no. 1, 144-153. https://doi.org/10.1016/j.jnt.2007.03.001
  2. E. B. Van Vleck, On the convergence of the continued fraction of Gauss and other con- tinued fractions, Ann. of Math. (2) 3 (1901/02), no. 1-4, 1-18. https://doi.org/10.2307/1967627
  3. E. B. Van Vleck, On the convergence of algebraic continued fractions whose coefficients have lim- iting values, Trans. Amer. Math. Soc. 5 (1904), no. 3, 253-262. https://doi.org/10.1090/S0002-9947-1904-1500672-9
  4. H. Waadeland, Tales about tails, Proc. Amer. Math. Soc. 90 (1984), no. 1, 57-64. https://doi.org/10.1090/S0002-9939-1984-0722415-5