Skip to main content
Springer Nature Link
Log in

Formal power series and their continued fraction expansion

  • Conference paper
  • First Online:
Algorithmic Number Theory (ANTS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1423))

Included in the following conference series:

  • 321 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Jean-Paul Allouche, Anna Lubiw, Michel Mendès France, Alf van der Poorten and Jeffrey Shallit, ‘Convergents of folded continued fractions', Acta Arith., 77 (1996), 77–96.

    MATH  MathSciNet  Google Scholar 

  2. J.-P. Allouche, M. Mendès France and A. J. van der Poorten, ‘An infinite product with bounded partial quotients', Acta Arith. 59 (1991), 171–182.

    MATH  MathSciNet  Google Scholar 

  3. L. Baum and M. Sweet, ‘Continued fractions of algebraic power series in characteristic 2', Ann. of Math. 103 (1976), 593–610.

    Article  MATH  MathSciNet  Google Scholar 

  4. Bruce C. Berndt, Ramanujan's notebooks, Springer-Verlag. Part I, with a foreword by S. Chandrasekhar, New York-Berlin, 1985; Part II, New York-Berlin, 1989; Part III, New York, 1991; Part IV, New York, 1994; Part V, New York, 1998.

    Google Scholar 

  5. T. G. Berry, ‘On periodicity of continued fractions in hyperelliptic function fields', Arch. Math. 55 (1990), 259–266.

    Article  MATH  MathSciNet  Google Scholar 

  6. Enrico Bombieri and Paula B. Cohen, 'siegel's Lemma, Padé Approximations and Jacobians’ (with an appendix by Umberto Zannier), to appear in the De Giorgi volume, Annali Scuola Normale Superiore, Pisa

    Google Scholar 

  7. David G. Cantor, ‘On the continued fractions of quadratic surds', Acta Arith. 68 (1994), 295–305.

    MATH  MathSciNet  Google Scholar 

  8. Michel Dekking, Michel Mendès France and Alf van der Poorten, ‘FOLDS!', The Mathematical Intelligencer 4 (1982), 130–138; II: 'symmetry disturbed', ibid. 173–181; III: ‘More morphisms', ibid. 190–195.

    Article  MATH  MathSciNet  Google Scholar 

  9. E. Dubois et R. Paysant-Le Roux, ‘Sur la longeur du developpement en fraction continue de √f(n)', Astérisque 198–200 (1991), 107–119

    Google Scholar 

  10. David Goss, David R. Hayes and Michael I. Rosen eds., The arithmetic of function fields, Proceedings of the workshop held at The Ohio State University, Columbus, Ohio, June 17–26, 1991. Ohio State University Mathematical Research Institute Publications, 2. Walter de Gruyter & Co., Berlin, 1992. viii+482 pp.

    MATH  Google Scholar 

  11. Peter Henrici, Applied and computational complex analysis, Vol. 2, Special functions—integral transforms—asymptotics—continued fractions. Reprint of the 1977 original. Wiley Classics Library. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1991. x+662 pp.

    Google Scholar 

  12. William B. Jones and Wolfgang J. Thron, Continued fractions. Analytic theory and applications, with a foreword by Felix E. Browder and an introduction by Peter Henrici. Encyclopedia of Mathematics and its Applications, 11. Addison-Wesley Publishing Co., Reading, Mass., 1980. xxix+428 pp.

    Google Scholar 

  13. Alain Lasjaunias, ‘Diophantine approximation and continued fractions expansions of algebraic power series in positive characteristic', J. Number Theory 65 (1997), 206–225.

    Article  MATH  MathSciNet  Google Scholar 

  14. Michel Mendès France, ‘Sur les fractions continues limitées', Acta Arith. 23 (1973), 207–215.

    MATH  MathSciNet  Google Scholar 

  15. M. Mendès France and A. J. van der Poorten, ‘From geometry to Euler identities', Theoretical Computing Science 65 (1989), 213–220.

    Article  MATH  Google Scholar 

  16. M. Mendès France and A. J. van der Poorten, ‘Some explicit continued fraction expansions', Mathematika 38 (1991), 1–9.

    Article  MATH  MathSciNet  Google Scholar 

  17. Michel Mendès France, Alf van der Poorten and Jeffrey Shallit, ‘On lacunary formal power series and their continued fraction expansion', to appear in the Proceedings of the Number Theory Conference in honour of Andrzej Schinzel on the occasion of his 60th birthday, K. Gyóry, H. Iwaniec and J. Urbanowicz eds, 6pp.

    Google Scholar 

  18. A. J. van der Poorten, ‘An introduction to continued fractions', in J. H. Loxton and A. J. van der Poorten eds., Diophantine Analysis (Cambridge University Press, 1986), 99–138.

    Google Scholar 

  19. A. J. van der Poorten and J. Shallit, ‘Folded continued fractions', J. Number Theory 40 (1992), 237–250.

    Article  MATH  MathSciNet  Google Scholar 

  20. A. J. van der Poorten and J. Shallit, ‘A specialised continued fraction', Canad. J. Math. 45 (1993), 1067–1079.

    MATH  MathSciNet  Google Scholar 

  21. G. N. Raney, ‘On continued fractions and finite automata', Math. Ann. 206 (1973), 265–283.

    Article  MATH  MathSciNet  Google Scholar 

  22. A. Schinzel, ‘On some problems of the arithmetical theory of continued fractions', Acta Arith. 7 (1962), 287–298.

    MATH  MathSciNet  Google Scholar 

  23. H. S. Wall, Analytic Theory of Continued Fractions, D. Van Nostrand Company, Inc., New York, N. Y., 1948; xiii+433 pp.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre for Number Theory Research, Macquarie University, Sydney

    Alf van der Poorten

Authors
  1. Alf van der Poorten
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Joe P. Buhler

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

van der Poorten, A. (1998). Formal power series and their continued fraction expansion. In: Buhler, J.P. (eds) Algorithmic Number Theory. ANTS 1998. Lecture Notes in Computer Science, vol 1423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054875

Download citation

  • DOI: https://doi.org/10.1007/BFb0054875

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64657-0

  • Online ISBN: 978-3-540-69113-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics