Vertical Shift and Simultaneous Diophantine Approximation on Polynomial Curves

Faustin Adiceam*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The Hausdorff dimension of the set of simultaneously τ-well-approximable points lying on a curve defined by a polynomial P(X) + α, where P(X) ∈ ℤ[X] and α ∈ ℝ, is studied when τ is larger than the degree of P(X). This provides the first results related to the computation of the Hausdorff dimension of the set of well-approximable points lying on a curve that is not defined by a polynomial with integer coefficients. The proofs of the results also include the study of problems in Diophantine approximation in the case where the numerators and the denominators of the rational approximations are related by some congruential constraint.

Original languageEnglish
Number of pages26
JournalProceedings of the Edinburgh Mathematical Society
Issue number1
Early online date27 Oct 2014
Publication statusPublished - Feb 2015


  • diophantine approximation
  • manifolds
  • metric theory
  • polynomial curves

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