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July 26, 2026Selecta MathematicaOpen Access

Bad approximability, bounded ratios and Diophantine exponents

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Authors

AMAntoine MarnatNMNikolay MoshchevitinJSJohannes Schleischitz

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Overview

Investigates the relationship between bad approximability and bounded ratios in Diophantine approximations, suggesting mathematical implications.

Key Points

  • To explore the equivalence between bad approximability of matrices and the boundedness of specific ratios in Diophantine approximations.
  • Consideration of best Diophantine approximation vectors in an n×m matrix
  • Analysis of sequences of norms for approximation vectors and remainders
  • Examination of special cases for m=1 and n=1 to establish equivalences
  • For m=1, bad approximability is equivalent to boundedness of ratios X(i+1)/X(i)
  • For n=1, it is equivalent to boundedness of ratios L(i)/L(i+1)
  • Examples illustrate these equivalences under specific conditions

Cite This Study

Marnat et al. (2026) studied this question.

synapsesocial.com/papers/6a65a2e2d3aea3239cd762a0https://doi.org/10.1007/s00029-026-01168-4
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