Abstract:
 Wirsing conjectured ( generalization of Dirichlet's result ) that for any real number $\zeta$ and positive integer $n$,
if $\zeta $ is not algebraic of degree at most $n$, then for any $\epsilon >0$, there exist infinitely many real algebraic numbers $\alpha$ with degree at most $n$
such that $ \zeta  \alpha  \leq \frac{C}{H(\alpha)^{n+1\epsilon }},$ where $C$ is a constant depending only on $\zeta$, $n$ and $\epsilon $. Sprind\v{z}uk showed that the conjecture is true for almost
all real numbers ( in the sense of Lebesgue measure).
Baker and Schmidt studied sets $K_n(\lambda)$ that are defined more widely in terms of approximation by algebraic approximation of bounded degrees and
established a generalization result of the JarnikBesicovitch theorem. In this talk we will give an analog of Baker and Schmidt's theorem in the fields of
formal power series.
