Nous décrivons un panorama des méthodes reliant l'étude des équations diophantiennes ternaires aux techniques modernes issues de la théorie des formes modulaires.
We give a survey of methods used to connect the study of ternary diophantine equations to modern techniques coming from the theory of modular forms.
@article{JTNB_1999__11_1_173_0, author = {Merel, Lo{\"\i}c}, title = {Arithmetic of elliptic curves and diophantine equations}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {173--200}, publisher = {Universit\'e Bordeaux I}, volume = {11}, number = {1}, year = {1999}, mrnumber = {1730439}, zbl = {0964.11028}, language = {en}, url = {http://www.numdam.org/item/JTNB_1999__11_1_173_0/} }
TY - JOUR AU - Merel, Loïc TI - Arithmetic of elliptic curves and diophantine equations JO - Journal de théorie des nombres de Bordeaux PY - 1999 SP - 173 EP - 200 VL - 11 IS - 1 PB - Université Bordeaux I UR - http://www.numdam.org/item/JTNB_1999__11_1_173_0/ LA - en ID - JTNB_1999__11_1_173_0 ER -
Merel, Loïc. Arithmetic of elliptic curves and diophantine equations. Journal de théorie des nombres de Bordeaux, Tome 11 (1999) no. 1, pp. 173-200. http://www.numdam.org/item/JTNB_1999__11_1_173_0/
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