Thue's Fundamentaltheorem, II: Further Refinements and Examples

Abstract

In this paper, we sharpen and simplify our earlier results based on Thue's Fundamentaltheorem and use it to obtain effective irrationality measures for certain roots of polynomials of the form $(x-\sqrt{t})^{n}+(x+\sqrt{t})^{n}$, where $n \geq 4$ is a positive integer and $t$ is a negative integer. For $n=4$ and $n=5$, we find infinitely many such algebraic numbers.