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arXiv · 1409.6665

There is no analogue to Jarník's relation for twisted Diophantine approximmation

Antoine Marnat
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Abstract

Jarník's relation is in dimension $2$ the formula $\hatλ + \frac{1}{\hatω} = 1$ linking both uniform exponents. It is an open question to generalize this equation to higher dimension, or to the multiplicative case. In this paper we consider a twisted case, between the classical and the multiplicative one, and we show that no analogue to Jarník's relation holds.

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Antoine Marnat. 2017-07-10. There is no analogue to Jarník's relation for twisted Diophantine approximmation. https://doi.org/10.1007/s00605-015-0859-8

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