On arithmetic properties of the convergents of Euler's number

C. Elsner

Colloquium Mathematicae (1999)

  • Volume: 79, Issue: 1, page 133-145
  • ISSN: 0010-1354

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Elsner, C.. "On arithmetic properties of the convergents of Euler's number." Colloquium Mathematicae 79.1 (1999): 133-145. <http://eudml.org/doc/210621>.

@article{Elsner1999,
author = {Elsner, C.},
journal = {Colloquium Mathematicae},
keywords = {best rational approximations; recurrence; periodic sequence; period length; Euler's number; continued fraction expansion; convergents; arithmetic properties; congruences},
language = {eng},
number = {1},
pages = {133-145},
title = {On arithmetic properties of the convergents of Euler's number},
url = {http://eudml.org/doc/210621},
volume = {79},
year = {1999},
}

TY - JOUR
AU - Elsner, C.
TI - On arithmetic properties of the convergents of Euler's number
JO - Colloquium Mathematicae
PY - 1999
VL - 79
IS - 1
SP - 133
EP - 145
LA - eng
KW - best rational approximations; recurrence; periodic sequence; period length; Euler's number; continued fraction expansion; convergents; arithmetic properties; congruences
UR - http://eudml.org/doc/210621
ER -

References

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  1. [1] H. Alzer, On rational approximations to e, J. Number Theory 68 (1998), 57-62. Zbl0913.11029
  2. [2] C. Elsner, On the approximation of irrational numbers with rationals restricted by congruence relations, Fibonacci Quart. 34 (1996), 18-29. 
  3. [3] C. Elsner, A metric result concerning the approximation of real numbers by continued fractions, ibid. 36 (1998), 290-294. Zbl0933.11038
  4. [4] C. Elsner, On the approximation of irrationals by rationals, Math. Nachr. 189 (1998), 243-256. Zbl0896.11027
  5. [5] L. Euler, De fractionibus continuis, Commentarii Academiae Scientiarum Imperialis Petropolitanae, 1737. 
  6. [6] S. Hartman, Sur une condition supplémentaire dans les approximations diophantiques, Colloq. Math. 2 (1949), 48-51. Zbl0038.18802
  7. [7] M. Hata, A lower bound for rational approximations to π, J. Number Theory 43 (1993), 51-67. 
  8. [8] M. Hata, Improvement in the irrationality measures of π and π^2 , Proc. Japan Acad. Ser. A Math. Sci. 68 (1992), 283-286. 
  9. [9] C. Hermite, Sur la fonction exponentielle, C. R. Acad. Sci. Paris 77 (1873), 18-24, 74-79, 226-233, 285-293. 
  10. [10] C. L. F. von Lindemann, Über die Zahl π, Math. Ann. 20 (1882), 213-225. 
  11. [11] K. Mahler, On the approximation of π, Proc. Akad. Wetensch. Ser. A 56 (1953), 30-42. Zbl0053.36105
  12. [12] 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
  13. [13] O. Perron, Die Lehre von den Kettenbrüchen, Chelsea, New York, 1950. Zbl0041.18206
  14. [14] T. Schneider, Einführung in die transzendenten Zahlen, Springer, Berlin, 1957. Zbl0077.04703
  15. [15] A. B. Shidlovskiĭ, Transcendental Numbers, de Gruyter, Berlin, 1989. 
  16. [16] S. Uchiyama, On rational approximations to irrational numbers, Tsukuba J. Math. 4 (1980), 1-7. Zbl0467.10023

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