Cubic Thue inequalities with negative discriminant

JOURNAL OF NUMBER THEORY

卷:97

Article

Wakabayashi, I

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

DOI  :  10.1016/S0022-314X(02)00010-0

来源: Elsevier

【 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.

【 授权许可】

Free