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Journal

Uniform Distribution Theory (UDT)


Volume & Issue

UDT. Volume 19. Issue 1 & 2


Published on

December, 2024


Pages

97-120


DOI

https://doi.org/10.2478/udt-2024-0008

Article

Uniform Dual Approximation to Veronese Curves in Small Dimension


Authors

Johannes Schleischitz


Abstract

We refine upper bounds for the classical exponents of uniform approximation for a linear form on the Veronese curve in dimension from 3 to 9. For dimension three, this in particular shows that a bound previously obtained by two different methods is not sharp. Our proof involves parametric geometry of numbers and investigation of geometric properties of best approximation polynomials. Slightly stronger bounds have been obtained by Poels with a different method contemporarily. In fact, we obtain his bounds as a conditional result.


Citation

Schleischitz, J. (2024). Uniform Dual Approximation to Veronese Curves in Small Dimension. Uniform distribution theory, 19(1-2), 97-120. https://doi.org/10.2478/udt-2024-0008