Speaker : Dr.Huei Jeng Chen (Acadamia Sinica)
Title : Approximation by algebraic elements of bounded degree in finite characteristic
Time : 2012-12-25 (Tue) 10:00 -
Place : Seminar Room 617, Institute of Mathematics (NTU Campus)
Abstract: Wirsing conjectured ( generalization of Dirichlet's result ) that for any real number and positive integer , if is not algebraic of degree at most , then for any , there exist infinitely many real algebraic numbers with degree at most such that where is a constant depending only on , and . 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 that are defined more widely in terms of approximation by algebraic approximation of bounded degrees and established a generalization result of the Jarnik-Besicovitch theorem. In this talk we will give an analog of Baker and Schmidt's theorem in the fields of formal power series.