Cubic Thue inequalities with negative discriminant

[摘要] We give an upper bound for the solutions of the family of cubic Thue inequalities \x(3) + axy(2) + by(3) \ less than or equal to k when a is positive and larger than a certain value depending on b. For the case k = a + \b\ + I and a greater than or equal to 360b(4) we show that these inequalities have only trivial solutions. For the case k = a + \b\ + I and \b\ = 1, 2, we solve these inequalities for all a greater than or equal to 1. Our method is based on Pade approximations using Rickert's integrals. We also use a generalization of Legendre's theorem on continued fractions. (C) 2002 Elsevier Science (USA). All rights reserved.

[发布日期] 2002-12-01

[关键词] Thue equation;Thue inequality;Pade approximation;continued fraction;Legendre's theorem