Thue's Fundamentaltheorem, II: Further Refinements and Examples
Paul Voutier

TL;DR
This paper refines Thue's Fundamentaltheorem to derive effective irrationality measures for specific algebraic numbers generated by polynomial roots, particularly for cases where n=4 and 5, revealing infinitely many such numbers.
Contribution
It provides new, sharper bounds and simplified methods based on Thue's theorem for measuring irrationality of certain algebraic numbers.
Findings
Effective irrationality measures for roots of specific polynomial forms
Infinite algebraic numbers identified for n=4 and n=5
Simplified refinements of previous results
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 , where is a positive integer and is a negative integer. For and , we find infinitely many such algebraic numbers.
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