Speaker : Dr.Huei Jeng Chen (Acadamia Sinica)
Title : Diophantine approximation and Hausdorff dimension in positive characteristic
Time : 2012-09-18 (Tue) 15:00 - 16:00
Place : Seminar Room 722, Institute of Mathematics (NTU Campus)
Abstract: For , let denotes the distance of from the nearest integer. Mahler (1932) conjectured that almost all real numbers has the following property (equivalent to Mahler's original conjecture by a classical transference principle ): for any positive integer and any there exist only finitely many integral polynomials with degree such that

where denotes the height of Sprinduk (1962) finally succeeded in establishing Mahler's conjecture. Later (1966) Baker gave a more precise results different from using a modified version of Sprinduk's method. In the first talk I will give an analogue of Baker's theorem in positive characteristic. In the next talk we will investigate the sets related to the approximation by algebraic elements of bounded degrees. Baker-Schmidt's theorem derive the Hausdorff dimension of these sets. We will prove Baker-Schmidt's theorem for function field version via the three crucial Lemmas: Baker's theorem, Minkowski's geometry numbers and reguler system.