We exactly determine the integral solutions to a previously untreated infinite family of cubic Thue equations of the form with at least such solutions. Our approach combines elementary arguments, with lower bounds for linear forms in logarithms and lattice-basis reduction.
Nous déterminons les solutions entières d’une nouvelle famille infinie d’équations de Thue cubiques, chacune de ces équations ayant exactement cinq solutions. Notre approche combine des arguments élémentaires avec des limites inférieures pour les formes linéaires en logarithmes et la réduction .
Michael A. Bennett 1; Amir Ghadermarzi 1
@article{JTNB_2015__27_2_389_0, author = {Michael A. Bennett and Amir Ghadermarzi}, title = {Extremal families of cubic {Thue} equations}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {389--403}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {27}, number = {2}, year = {2015}, doi = {10.5802/jtnb.907}, mrnumber = {3393160}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.907/} }
TY - JOUR AU - Michael A. Bennett AU - Amir Ghadermarzi TI - Extremal families of cubic Thue equations JO - Journal de théorie des nombres de Bordeaux PY - 2015 SP - 389 EP - 403 VL - 27 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.907/ DO - 10.5802/jtnb.907 LA - en ID - JTNB_2015__27_2_389_0 ER -
%0 Journal Article %A Michael A. Bennett %A Amir Ghadermarzi %T Extremal families of cubic Thue equations %J Journal de théorie des nombres de Bordeaux %D 2015 %P 389-403 %V 27 %N 2 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.907/ %R 10.5802/jtnb.907 %G en %F JTNB_2015__27_2_389_0
Michael A. Bennett; Amir Ghadermarzi. Extremal families of cubic Thue equations. Journal de théorie des nombres de Bordeaux, Volume 27 (2015) no. 2, pp. 389-403. doi : 10.5802/jtnb.907. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.907/
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