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 $n\ge 4$ is a positive integer and $t$ is a negative integer. For $n=4$ and $n=5$, we find infinitely many such algebraic numbers.

arXiv commentcorrections to accepted version

References in corpus (4)

• Complete solution of the diophantine equation $X^2+1=d{Y}^4$ and a related family of quartic Thue equations
• Thue's Fundamentaltheorem, I: The General Case
• Rational approximations to $\sqrt[3]{2}$ and other algebraic numbers revisited
• Effective Irrationality Measures and Approximation by Algebraic Conjugates

Cited by in corpus (2)

• Bounds on the number of squares in recurrence sequences
• Improved Constants for Effective Irrationality Measures from Hypergeometric Functions