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An improved bound in Wirsing's problem
Dzmitry Badziahin, Johannes Schleischitz
We improve the lower bound for the classical exponent of approximation connected to Wirsing's famous problem of approximation to real numbers by algebraic numbers…
On geometry of numbers and uniform rational approximation to the Veronese curve
Johannes Schleischitz
Consider the classical problem of rational simultaneous approximation to a point in . The optimal lower bound on the gap between the induced ordinary and uniform ap…
On simultaneous rational approximation to a real number and its integral powers, II
Dmitry Badziahin, Yann Bugeaud
For a positive integer and a real number , let denote the supremum of the real numbers for which there are arbitrarily large positive integers such that $|…
Construction of numbers with almost all convergents in a Cantor set
Damien Roy, Johannes Schleischitz
In 1984, K. Mahler asked how well elements in the Cantor middle third set can be approximated by rational numbers from that set, and by rational numbers outside of that set. We con…
On a question of Schmidt and Summerer concerning -systems
Johannes Schleischitz
Following a suggestion of W.M. Schmidt and L. Summerer, we construct a proper -system with the property . In fact, our method generalizes…