A generalization of Perron's theorem about Hurwitzian numbers

Pierre Stambul

Acta Arithmetica (1997)

  • Volume: 80, Issue: 2, page 141-148
  • ISSN: 0065-1036

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Pierre Stambul. "A generalization of Perron's theorem about Hurwitzian numbers." Acta Arithmetica 80.2 (1997): 141-148. <http://eudml.org/doc/207033>.

@article{PierreStambul1997,
author = {Pierre Stambul},
journal = {Acta Arithmetica},
keywords = {Perron's theorem; Hurwitzian numbers; Möbius transformation; irrational numbers; continued fraction expansion},
language = {eng},
number = {2},
pages = {141-148},
title = {A generalization of Perron's theorem about Hurwitzian numbers},
url = {http://eudml.org/doc/207033},
volume = {80},
year = {1997},
}

TY - JOUR
AU - Pierre Stambul
TI - A generalization of Perron's theorem about Hurwitzian numbers
JO - Acta Arithmetica
PY - 1997
VL - 80
IS - 2
SP - 141
EP - 148
LA - eng
KW - Perron's theorem; Hurwitzian numbers; Möbius transformation; irrational numbers; continued fraction expansion
UR - http://eudml.org/doc/207033
ER -

References

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  1. [1] H. Cabannes, Étude des fractions continues ayant leurs quotients en progression arithmétique ou en progression géométrique, La Revue Scientifique 83 (1945), 230-233. Zbl0060.16201
  2. [2] C. S. Davis, On some simple continued fractions connected with e, J. London Math. Soc. 20 (1945), 194-198. Zbl0060.16111
  3. [3] L. Euler, De fractionibus continuis dissertatio, Comment. Acad. Petropol. 9 (1744), 115-127. 
  4. [4] D. H. Lehmer, Continued fractions containing arithmetic progressions, Scripta Math. 29 (1973), 17-24. Zbl0263.10012
  5. [5] P. Liardet et P. Stambul, Transducteurs et fractions continuées, preprint, 1996. 
  6. [6] K. R. Matthews and R. F. C. Walters, Some properties of the continued fraction expansion of m / n e 1 / q , Proc. Cambridge Philos. Soc. 67 (1970), 67-74. Zbl0188.10703
  7. [7] O. Perron, Die Lehre von den Kettenbrüchen, Bd. 1, 3rd ed., Teubner, 1954, 110-138. 
  8. [8] 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. Zbl0596.10008
  9. [9] G. Raney, On continued fractions and finite automata, Math. Ann. 206 (1973), 265-283. Zbl0251.10024
  10. [10] P. Stambul, Contribution à l'étude des propriétés arithmétiques des fractions continuées, Thèse de l'Université de Provence, 1994 

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