Minoration de combinaisons linéaires de deux logarithmes p -adiques

Dong Pingping

Annales de la Faculté des sciences de Toulouse : Mathématiques (1991)

  • Volume: 12, Issue: 2, page 195-250
  • ISSN: 0240-2963

How to cite

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Pingping, Dong. "Minoration de combinaisons linéaires de deux logarithmes $p$-adiques." Annales de la Faculté des sciences de Toulouse : Mathématiques 12.2 (1991): 195-250. <http://eudml.org/doc/73281>.

@article{Pingping1991,
author = {Pingping, Dong},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {Schneider's method; -adic logarithms; explicit lower bound; algebraic numbers with rational coefficients},
language = {fre},
number = {2},
pages = {195-250},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Minoration de combinaisons linéaires de deux logarithmes $p$-adiques},
url = {http://eudml.org/doc/73281},
volume = {12},
year = {1991},
}

TY - JOUR
AU - Pingping, Dong
TI - Minoration de combinaisons linéaires de deux logarithmes $p$-adiques
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1991
PB - UNIVERSITE PAUL SABATIER
VL - 12
IS - 2
SP - 195
EP - 250
LA - fre
KW - Schneider's method; -adic logarithms; explicit lower bound; algebraic numbers with rational coefficients
UR - http://eudml.org/doc/73281
ER -

References

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  1. [1] Gramain ( F.) et Mignotte ( M.) .— Fonctions entières arithmétiques, in Approximations diophantiennes et nombres transcendants, Birkhaüser, Progress in Math.31 (1983) pp. 99-124. Zbl0541.10029MR702192
  2. [2] Malher ( K.) .— Über transzendente P-adische Zahlen, Compositio Math.2 (1935) pp. 259-275. Zbl61.0187.01JFM61.0187.01
  3. [3] Mignotte ( M.) et Waldschmidt ( M.) .— Linear forms in two logarithms and Schneider's method, (I), Math. Ann.231 (1978) pp. 241-267; (II) Acta Arithm.53 (1989) pp. 251-287; (III) Ann. Fasc. Sci. Toulouse97 (1989) pp. 43-75. Zbl0702.11044MR1032827
  4. [4] Van Der Poorten ( A.J.) .— On Baker's inequality for linear forms in logarithms, Math. Proc. Camb. Phil. Soc.80 (1976) pp. 233-248. Zbl0341.10030MR417067
  5. [5] Van Der Poorten ( A.J.) . — Linear forms in logarithms in the p-adic case, Transcendence Theory : Advances and Applications; Academic Press1977, chap. 2, pp. 29-57. Zbl0367.10034MR498418
  6. [6] Schinzel ( A.) . — On two theorems of Gel 'fond and some of their applications, Acta Arithm.13 (1967) pp. 177-236. Zbl0159.07101MR222034
  7. [7] Serre ( J.P.) .— Dépendance d'exponentielles p-adiques, Sém. Delange-Pisot-Poitou, 7ème année, 1965/66, exposé 15. Zbl0254.10033
  8. [8] Shorey ( T.N.), Van Der Poorten ( A.J.), Tijdeman ( R.) and Schinzel ( A.) .— Applications of the Gel'fond-Baker method to diophantine equations, Transcendence Theory : Advances and Applications ; Academic Press, 1977, chap. 3, pp. 59-77. Zbl0371.10015MR472689
  9. [9] Kunrui ( Yu) .— Linear forms in p-adic logarithms, Acta. Arith.53 (1989) pp. 107-186. Zbl0699.10050MR1027200
  10. [10] Kunrui ( Yu) .— Linear forms in p-adic logarithms II, Compositio Math.74 (1990) pp. 15-113. Zbl0723.11034

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