Linear independence of continued fractions

Jaroslav Hančl

Journal de théorie des nombres de Bordeaux (2002)

  • Volume: 14, Issue: 2, page 489-495
  • ISSN: 1246-7405

Abstract

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The main result of this paper is a criterion for linear independence of continued fractions over the rational numbers. The proof is based on their special properties.

How to cite

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Hančl, Jaroslav. "Linear independence of continued fractions." Journal de théorie des nombres de Bordeaux 14.2 (2002): 489-495. <http://eudml.org/doc/248900>.

@article{Hančl2002,
abstract = {The main result of this paper is a criterion for linear independence of continued fractions over the rational numbers. The proof is based on their special properties.},
author = {Hančl, Jaroslav},
journal = {Journal de théorie des nombres de Bordeaux},
language = {eng},
number = {2},
pages = {489-495},
publisher = {Université Bordeaux I},
title = {Linear independence of continued fractions},
url = {http://eudml.org/doc/248900},
volume = {14},
year = {2002},
}

TY - JOUR
AU - Hančl, Jaroslav
TI - Linear independence of continued fractions
JO - Journal de théorie des nombres de Bordeaux
PY - 2002
PB - Université Bordeaux I
VL - 14
IS - 2
SP - 489
EP - 495
AB - The main result of this paper is a criterion for linear independence of continued fractions over the rational numbers. The proof is based on their special properties.
LA - eng
UR - http://eudml.org/doc/248900
ER -

References

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  1. [1] P. Bundschuh, Transcendental continued fractions. J. Number Theory18 (1984), 91-98. Zbl0531.10035MR734440
  2. [2] H. Davenport, K.F. Roth, Rational approximations to algebraic numbers. Mathematika2 (1955), 160-167. Zbl0066.29302MR77577
  3. [3] G.M. Fichtengolc, Lecture on Differential and lntegrational Calculus II (Russian). Fizmatgiz, 1963. 
  4. [4] J. Hancl, Linearly unrelated sequences. Pacific J. Math.190 (1999), 299-310. Zbl1005.11033MR1722896
  5. [5] J. Hancl, Continued fractional algebraic independence of sequences. Publ. Math. Debrecen46 (1995), 27-31. Zbl0862.11045MR1316646
  6. [6] G.H. Hardy, E.M. Wright, An Introduction to the Theory of Numbers. Oxford Univ. Press, 1985. Zbl0020.29201MR568909
  7. [7] H.P. Schlickewei, A.J. Van Der Poorten, The growth conditions for recurrence sequences. Macquarie University Math. Rep. 82-0041, North Ryde, Australia, 1982. 

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