Examples of badly approximable vectors over number fields
Robert Hines

TL;DR
This paper constructs examples of badly approximable vectors over number fields by exploring their approximation properties and linking them to compact subspaces associated with quadratic and Hermitian forms, generalizing classical results over rationals.
Contribution
It introduces a method to generate badly approximable vectors over number fields using compact subspaces related to quadratic and Hermitian forms, extending known results from rational numbers.
Findings
Examples of badly approximable vectors over number fields are constructed.
Connections between these vectors and compact subspaces of certain arithmetic quotients are established.
Generalization of quadratic irrational approximation properties to number fields.
Abstract
We consider approximation of vectors by elements of a number field and construct examples of badly approximable vectors. These examples come from compact subspaces of naturally associated to (totally indefinite, anisotropic) -rational binary quadratic and Hermitian forms, a generalization of the well-known fact that quadratic irrationals are badly approximable over .
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Taxonomy
TopicsMathematical Dynamics and Fractals · Mathematical Analysis and Transform Methods · Tensor decomposition and applications
