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

Abstract

Jarník's relation is in dimension $2$ the formula $\hat{\lambda }+\frac{1}{\hat{\omega }}=1$ 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.

15 pages

Cited by in corpus (1)

• Geometry of Diophantine exponents