Transcendence measures of exponentials and logarithms of algebraic numbers

P. L. Cijsouw

Compositio Mathematica (1974)

  • Volume: 28, Issue: 2, page 163-178
  • ISSN: 0010-437X

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Cijsouw, P. L.. "Transcendence measures of exponentials and logarithms of algebraic numbers." Compositio Mathematica 28.2 (1974): 163-178. <http://eudml.org/doc/89206>.

@article{Cijsouw1974,
author = {Cijsouw, P. L.},
journal = {Compositio Mathematica},
language = {eng},
number = {2},
pages = {163-178},
publisher = {Noordhoff International Publishing},
title = {Transcendence measures of exponentials and logarithms of algebraic numbers},
url = {http://eudml.org/doc/89206},
volume = {28},
year = {1974},
}

TY - JOUR
AU - Cijsouw, P. L.
TI - Transcendence measures of exponentials and logarithms of algebraic numbers
JO - Compositio Mathematica
PY - 1974
PB - Noordhoff International Publishing
VL - 28
IS - 2
SP - 163
EP - 178
LA - eng
UR - http://eudml.org/doc/89206
ER -

References

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  1. [1] P. Bundschuh: Zu einem Transzendenzsatz der Herren Baron und Braune, To appear in J. f.d. reine und angew. Math. Zbl0266.10028MR327675
  2. [2] P.L. Cijsouw: Transcendence measures. (Thesis) University of Amsterdam, 1972. Zbl0252.10031MR349596
  3. [3] N.I. Fel'dman: Approximation of certain transcendental numbers. I. The approximation of logarithms of algebraic numbers. (Russian) Izv. Akad. Nauk SSSR, ser. mat., 15 (1951) 53-74.English translation: Amer. Math. Soc. Transl., II ser., 59 (1966) 224-245. Zbl0199.09605MR39768
  4. [4] N.I. Fel'dman: Approximation of the logarithms of algebraic numbers by algebraic numbers. (Russian) Izv. Akad. Nauk SSSR, ser. mat., 24 (1960) 475-492.English translation: Amer. Math. Soc. Transl., II ser., 58 (1966) 125-142. Zbl0199.09602MR114805
  5. [5] N.I. Fel'dman: On the problem of the measure of transcendence of e.(Russian) Uspekhi Mat. Nauk18 (3) (1963) 207-213. MR154854
  6. [6] N.I. Fel'dman: Estimate for a linear form of logarithms of algebraic numbers. (Russian) Mat. Sbornik (N.S.) 76 (118)(1968) 304-319.English translation: Math. USSR Sbornik5 (1968) 291-307. Zbl0195.33701MR228445
  7. [7] A.I. Galočkin: On the diophantine approximation of values of the exponential function and of solutions of certain transcendental equations. (Russian)Vestnik Moskov. Univ., Ser. I, 27 (3) (1972) 16-23. Zbl0259.10035MR299560
  8. [8] A.O. Gel'fond: Transcendental and algebraic numbers. (translated from the first Russian edition) Dover Publ., New York1960. Zbl0090.26103MR111736
  9. [9] F. Lindemann, Ueber die Zahl π. Math. Ann.20 (1882) 213-225. JFM14.0369.04
  10. [10] K. Mahler: An application of Jensen's formula to polynomials. Mathematika7 (1960) 98-100. Zbl0099.25003MR124467
  11. [11] T. Schneider: Einführung in die Transzendenten Zahlen. Springer Verlag, Berlin1957. Zbl0077.04703MR86842
  12. [12] R. Tijdeman: On the algebraic independence of certain numbers. Nederl. Akad. Wet. Proc., ser A, 74 (1971) 146-162= Indag. Math.33 (1971) 146-162. Zbl0212.07103MR294264
  13. [13] R. Tijdeman: An auxiliary result in the theory of transcendental numbers. J. Number Th.5 (1973) 80-94. Zbl0254.10027MR316395
  14. [14] M. Waldschmidt: Un premier cours sur les nombres transcendants. To appear in the Lecture Notes in Mathematics, Springer Verlag, Berlin. Zbl0302.10030

Citations in EuDML Documents

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  1. Pieter L. Cijsouw, On the approximability of the logarithms of algebraic numbers
  2. P. L. Cijsouw, Transcendence measures of certain numbers whose transcendency was proved by A. Baker
  3. Maurice Mignotte, Michel Waldschmidt, Approximation simultanée de valeurs de la fonction exponentielle
  4. A. Bijlsma, On the simultaneous approximation of a , b and a b
  5. G. Diaz, Complément à : «Sur l’approximation de π par des nombres algébriques particuliers»
  6. Guy Diaz, Une nouvelle minoration de |logα - β|, |α - expβ|, α et β algébriques

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