Best simultaneous Diophantine approximations for some pairs of algebraic numbers
Gustavo Antonio Pavani
TL;DR
This paper computes the sequence of best Diophantine approximations for specific pairs of cubic Pisot numbers that lack Property (F), advancing understanding of their approximation properties.
Contribution
It provides explicit computations of best Diophantine approximations for certain algebraic number pairs previously not well-understood.
Findings
Explicit sequences of best approximations obtained.
Identification of pairs not satisfying Property (F).
Enhanced understanding of approximation behavior for these algebraic numbers.
Abstract
We compute the sequence of best Diophantine approximations for some pairs of cubic Pisot numbers which do not satisfy the Property (F).
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Taxonomy
TopicsMathematical Dynamics and Fractals · Analytic Number Theory Research · Algebraic Geometry and Number Theory