|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)|
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.