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math.NT2024★ 1 cited
Uniform dual approximation to Veronese curves in small dimension
Johannes Schleischitz
We refine upper bounds for the classical exponents of uniform approximation for a linear form on the Veronese curve in dimension from to . For dimension three, this in parti…
math.NT2024
Maillet's property and Mahler's Conjecture on Liouville numbers fail for matrices
Johannes Schleischitz
In the early 1900's, Maillet proved that the image of any Liouville number under a rational function with rational coefficients is again a Liouville number. The analogous result fo…
math.NT2024
On the Folklore set and Dirichlet spectrum for matrices
Mumtaz Hussain, Johannes Schleischitz, Benjamin Ward
We study the Folklore set of Dirichlet improvable matrices in which are neither singular nor badly approximable. We prove the non-emptiness for all positive…