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

Abstract : Jarník gave a relation between the two most classical uniform exponents of Diophantine approximation in dimension 2. 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. There is no analogue to Jarník's relation for twisted Diophantine approximation. Monatshefte für Mathematik, Springer Verlag, 2016, 181, pp.675 - 688. ⟨10.1007/s00605-015-0859-8⟩. ⟨hal-01398025⟩

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