Abstract. We improve on Jarník's inequality between uniform Diophantine exponent $\alpha $ and ordinary Diophantine exponent $\beta $ for a system of $ n\ge2$ real linear forms in two integer variables. Jarník (1949, 1954) proved that $\beta\ge \alpha(\alpha -1)$. In the present paper we give a better bound in the case $\alpha >1$.
AMS Subject Classification
(1991): 11J13
Keyword(s):
Diophantine exponents,
linear forms,
best approximations
Received September 11, 2012, and in revised form February 6, 2012. (Registered under 68/2012.)
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