Simultaneous Diophantine approximation for algebraic functions in positive characteristic (Q1181781)

The author studies simultaneous diophantine approximations of a pair \((\alpha,\beta)\) of quadratic formal series in positive characteristic. For each real number \(\mu\), put \(B(\alpha,\beta,\mu)=\lim\inf| Q|^ \mu\| Q\alpha\| \| Q\beta\|\) (when \(Q\) runs amongs polynomials of strictly increasing degrees). He first shows that if \(\nu\) is the approximation exponent of \((\alpha,\beta)\), one has \(B(\alpha,\beta,\nu)>0\) (and \(B(\alpha,\beta,\nu)=0\) if \(\mu<\nu\), and \(=+\infty\) if \(\mu>\nu\)). So a pair \((\alpha,\beta)\) of quadratic formal series satisfies Littlewood's hypothesis \(B(\alpha,\beta,1)=0\) if and only if \(\nu>1\). Then he proves that for formal series over a finite field of characteristic 2, one has \(\nu>1\) for each pair of quadratics. The problem is unsolved for other characteristics, but it is possible to treat examples.