Effective diophantine approximation on 𝔾 m

Enrico Bombieri

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1993)

  • Volume: 20, Issue: 1, page 61-89
  • ISSN: 0391-173X

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Bombieri, Enrico. "Effective diophantine approximation on $\mathbb {G}_m$." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 20.1 (1993): 61-89. <http://eudml.org/doc/84143>.

@article{Bombieri1993,
author = {Bombieri, Enrico},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {irrationality measures; effective solution of Thue equation; theorem of Baker-Fel'dman; Liouville's theorem; multiplicative group; generalized Siegel's unit equation},
language = {eng},
number = {1},
pages = {61-89},
publisher = {Scuola normale superiore},
title = {Effective diophantine approximation on $\mathbb \{G\}_m$},
url = {http://eudml.org/doc/84143},
volume = {20},
year = {1993},
}

TY - JOUR
AU - Bombieri, Enrico
TI - Effective diophantine approximation on $\mathbb {G}_m$
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1993
PB - Scuola normale superiore
VL - 20
IS - 1
SP - 61
EP - 89
LA - eng
KW - irrationality measures; effective solution of Thue equation; theorem of Baker-Fel'dman; Liouville's theorem; multiplicative group; generalized Siegel's unit equation
UR - http://eudml.org/doc/84143
ER -

References

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  7. [Bo-M] E. Bombieri - J. Mueller, On effective measures of irrationality for √a/b and related numbers, J. Reine Angew. Math., 342 (1983), 173-196. Zbl0516.10024
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  12. [F] N.I. Feldman, An effective refinement in the exponent in Liouville's theorem (Russian), Izv. Akad. Nauk SSSR Ser. Mat., 35 (1971), 985-1002. Zbl0259.10031MR289418
  13. [G] A.O. Gelfond, Transcendental and algebraic numbers. English translation by L.F. Boron, Dover Publications Inc., New York1960. Zbl0090.26103MR111736
  14. [G-P] K. Györy - Z.Z. Papp, Norm form equations and explicit lower bounds for linear forms with algebraic coefficients, Studies in Pure Mathematics (to the memory of Paul Turán), Akadémiai Kiadó, Budapest and Birkhäuser Verlag, Basel1983, 245-257. Zbl0518.10020MR820227
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  16. [M] K. Mahler, Zur Approximation algebraischer Zahlen (I). Über den grössten Primteiler binärer Formen, Math. Ann., 107 (1933), 691-730. Zbl0006.10502MR1512822JFM59.0220.01
  17. [S] C.L. Siegel, Über einige Anwendungen diophantischer Approximationen, Abh. Preuß. Akad. Wissen. Phys.-Math. Kl. (1929) 1, 1-70.Also Gesammelte Abhandlungen, Springer-Verlag, Berlin-Heidelberg -New York1966, Bd. I, 209-274. JFM56.0180.05
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Citations in EuDML Documents

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  1. E. Bombieri, P. B. Cohen, Effective diophantine approximation on 𝔾 M , II
  2. Yuri Bilu, Yann Bugeaud, Démonstration du théorème de Baker-Feldman via les formes linéaires en deux logarithmes
  3. Yann Bugeaud, Kálmán Győry, Bounds for the solutions of Thue-Mahler equations and norm form equations
  4. Pietro Corvaja, Une application nouvelle de la méthode de Thue
  5. E. Bombieri, A. J. Van der Poorten, J. D. Vaaler, Effective measures of irrationality for cubic extensions of number fields
  6. Enrico Bombieri, Diophantine Equations in Low Dimensions
  7. Yann Bugeaud, Kálmán Győry, Bounds for the solutions of unit equations

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