A note on Dirichlet spectrum
Renat K. Akhunzhanov, Nikolay G. Moshchevitin
TL;DR
This paper investigates properties of the Dirichlet spectrum concerning simultaneous approximation of two real numbers, focusing on their approximability characteristics in Euclidean space.
Contribution
It provides a new theoretical result relating Dirichlet spectrum to the approximation quality of two real numbers, especially in cases of badly or well approximable numbers.
Findings
Established a connection between Dirichlet spectrum and approximation quality.
Characterized the spectrum for badly and well approximable pairs.
Extended understanding of simultaneous Diophantine approximation.
Abstract
We prove a result related to Dirichlet spectrum for simultaneous approximation to two real numbers in Euclidean norm and badly or very well approximability.
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Taxonomy
TopicsMathematical Approximation and Integration · Mathematical Analysis and Transform Methods · Approximation Theory and Sequence Spaces