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Majorations Effectives Pour L’ Équation de Fermat Généralisée

Published online by Cambridge University Press:  20 November 2018

Alain Kraus
Alain Kraus*
Affiliation:
Université de Paris VI, Institut de Mathématiques, Case 247, 4, place Jussieu, 75252 Paris Cedex 05, France
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Abstract

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Keywords

11G
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 6 , 01 December 1997 , pp. 1139 - 1161
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Apostol, T.M., Introduction to Analytic Number Theory. Undergraduate Texts in Math., Springer-Verlag, 1976.Google Scholar
2. Atkin, A.O.L. et Lehner, J., Hecke operators on Γ0(N). Math. Ann. 185(1970), 134–160.Google Scholar
3. Cremona, J.E., Algorithms for modular elliptic curves. Cambridge University Press, 1992.Google Scholar
4. Darmon, H., Serre's conjectures. Seminar on Fermat's Last Theorem (Ed.: Kumar Murty, V.), CMS Conference Proceedings 17(1995), 135–153.Google Scholar
5. Darmon, H. et L.Merel,Winding quotients and some variants of Fermat's last Theorem. J. Crelle 490(1997).Google Scholar
6. Deligne, P., La conjecture de Weil. I, Publ. Math. I.H.E.S. 43(1973), 273–307.Google Scholar
7. Deligne, P., Représentations l-adiques. S.M.F, Astérisque, 127(1985), 249–255.Google Scholar
8. Dénes, P., Über die Diophantische Gleichung xl + yl = czl. Acta Math. 88(1952), 241–251.Google Scholar
9. Diamond, F., On deformation rings and Hecke rings. Ann. of Math. 144(1996), 137–166.Google Scholar
10. Diamond, F. et Kramer, K., Modularity of a family of elliptic curves. Math. Res. Lett. 2(1995), 299–304.Google Scholar
11. Frey, G., Links between solutions of A - B = C and elliptic curves. Lecture Notes in Math. 13801989, 31–62.Google Scholar
12. Frey, G., On elliptic curves with isomorphic torsion structures and corresponding curves of genus 2. Dans : Elliptic Curves, Modular Forms, & Fermat's Last Theorem (Rédacteurs : Coates, J. et Yau, S.T.), International Press, 1995.Google Scholar
13. Hijikata, H., Explicit formula of the traces of Hecke operators for Γ0(N). J. Math. Soc. Japan 26(1974), 56–82.Google Scholar
14. Koblitz, N., Introduction to Elliptic Curves and Modular Forms. Graduate Texts in Math. 97, Springer- Verlag, 1984.Google Scholar
15. Kraus, A., Sur le défaut de semi-stabilité des courbes elliptiques à réduction additive. Manuscripta Math. 69(1990), 353–385.Google Scholar
16. Kraus, A., Une remarque sur les points de torsion des courbes elliptiques. C.R. Acad. Sci. Paris t. 321Série I(1995), 1143–1146.Google Scholar
17. Kraus, A., Détermination du poids et du conducteur associés aux représentations des points de p-torsion d’une courbe elliptique. Dissertationes Math. 364(1997), 39 pp.Google Scholar
18. Kraus, A. et Oesterlé, J., Sur une question de B. Mazur. Math. Ann. 293(1992), 259–275.Google Scholar
19. Mestre, J.-F., La méthode des graphes. Exemples et applications. Taniguchi Symp., Kyoto, 1986. 217–242.Google Scholar
20. Oesterlé, J., Nouvelles approches du “théorème de Fermat”. Sém. Bourbaki 694, 1987–88.Google Scholar
21. Ribet, K., On the equation ap + 2αbp + cp = 0. Acta Arith., à paraître.Google Scholar
22. Serre, J.-P., Propriétés galoisiennes des points d’ordre fini des courbes elliptiques. Invent. Math. 15(1972), 259–331.Google Scholar
23. Serre, J.-P., Modular forms of weight one and Galois representations. Algebraic Number Theory (Rédacteur : Fröhlich, A.), New York, Academic Press, 1977. 193–268.Google Scholar
24. Serre, J.-P., Sur les représentations modulaires de degré 2 de Gal (ℚ/ ℚ), Duke Math. J. 54(1987), 179–230.Google Scholar
25. Serre, J.-P., Abelian l-Adic Representations and Elliptic Curves. Advanced book classics series, Addison- Wesley, 1989.(publié originalement en 1968 par Benjamin, W.A., Inc.).Google Scholar
26. Serre, J.-P., Travaux de Wiles (et Taylor, …), I. Sém. Bourbaki 803, 1994–95.Google Scholar
27. Shimura, G., Introduction to the Arithmetic Theory of Automorphic Functions. Publ. Math. Soc. Japan 11, Princeton Univ. Press, 1971.Google Scholar
28. Silverman, J., The Arithmetic of Elliptic Curves. Graduate Texts in Math. 106, Springer-Verlag, 1986.Google Scholar
29. Tate, J., Algorithm for determining the type of a singular fiber in an elliptic pencil. Dans :Modular Functions of One Variable IV, Lecture Notes in Math. 476(1975), 33–52.Google Scholar
30. Wiles, A., Modular elliptic curves and Fermat's Last Theorem. Ann. of Math. 141(1995), 443–551.Google Scholar