Thue's Fundamentaltheorem, II: Some New Irrationality Measures

Details Thue's Fundamentaltheorem, II: Some New Irrationality Measures Thue's Fundamentaltheorem, II: Some New Irrationality Measures

2009-01-12

arxiv.org/abs/0901.1637v1

Mathematics

Number Theory

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Scientific paper

In this paper, we apply Thue's Fundamentaltheorem to obtain effective
irrationality measures for certain roots of particular 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
numbers.

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