代数数的有理逼近及其在求解丢番图方程中的应用

摘要

In this paper, the method of Thue and Siegel, based on explict Pade approximations to algebraic functions, are used to examine diophantine approximations to certain algebraic numbers. Effective improvements over Liouville theorem are preceneted for a class of algebraic number of degree 4, finally, the results have been used to solve diophantime equation ax2-by4=-1.%在本文中,我们利用Thue-Sieqel方法研究一类代数数的有理逼近,证明了对此类代数数的有效有一逼近,最后我们利用此结果研究了diophantine方程.ax2-by4=-1得出关于此方程完整的结论.