Diophantine exponents for systems of linear forms in two variables
NG Moshchevitin�- Acta Scientiarum Mathematicarum, 2013 - Springer
NG Moshchevitin
Acta Scientiarum Mathematicarum, 2013•SpringerWe improve on Jarn�k's inequality between uniform Diophantine exponent α and ordinary
Diophantine exponent β for a system of n≥ 2 real linear forms in two integer variables.
Jarn�k (1949, 1954) proved that β≥ α (α-1). In the present paper we give a better bound in
the case α< 1.
Diophantine exponent β for a system of n≥ 2 real linear forms in two integer variables.
Jarn�k (1949, 1954) proved that β≥ α (α-1). In the present paper we give a better bound in
the case α< 1.
Abstract
We improve on Jarn�k’s inequality between uniform Diophantine exponent α and ordinary Diophantine exponent β for a system of n ≥ 2 real linear forms in two integer variables. Jarn�k (1949, 1954) proved that β ≥ α(α - 1). In the present paper we give a better bound in the case α < 1.
Springer