Proceedings of the Japan Academy, Series A, Mathematical Sciences

Quadratic relations between logarithms of algebraic numbers

Damien Roy and Michel Waldschmidt

Full-text: Open access

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci. Volume 71, Number 7 (1995), 151-153.

Dates
First available in Project Euclid: 19 November 2007

Permanent link to this document
http://projecteuclid.org/euclid.pja/1195510604

Digital Object Identifier
doi:10.3792/pjaa.71.151

Mathematical Reviews number (MathSciNet)
MR1363903

Zentralblatt MATH identifier
0860.11040

Subjects
Primary: 11J85: Algebraic independence; Gelʹfond's method

Citation

Roy, Damien; Waldschmidt, Michel. Quadratic relations between logarithms of algebraic numbers. Proc. Japan Acad. Ser. A Math. Sci. 71 (1995), no. 7, 151--153. doi:10.3792/pjaa.71.151. http://projecteuclid.org/euclid.pja/1195510604.


Export citation

References

  • [1] Brownawell, W. D.: The algebraic independence of certain numbers related to the exponential function. J. Number Th., 6, 22-31 (1974).
  • [2] Fel'dman, N. I.: Hilbert's seventh problem. Moscow, Moscow State University, pp. 1-311 (1982).
  • [3] Gel'fond, A. O.: Transcendental Number Theory. Moscow (1952); Engl, transl., Dover Publ., N. Y. (1960).
  • [4] Laurent, M.: Sur quelques resultats recents de transcendance. Journees arithmetiques Luminy, 1989. Asterisque 198-200, 209-230 (1991).
  • [5] Philippon, P.: Lemme de zeros dans les groupes algebriques commutatifs: Bull. Soc. Math. France, 114, 355-383 (1986); 115, 397-398 (1987).
  • [6] Waldschmidt, M.: Solution du huitieme probleme de Schneider. J. Number Th., 5, 191-202 (1973).
  • [7] Waldschmidt, M.: Linear Independence of Logarithms of Algebraic Numbers. IMSc Report, no 116, The Institute of Mathematical Sciences, Madras. (1992).
  • [8] Wirsing, E.: Approximation mit algebraischen Zahlen beschrankten Grades. J. r. angew. Math. (Crelle), 206, 67-77 (1961).