Seminar in Number Theory

主講者: | 陳慧錚博士 (中研院數學所) |

講題: | Approximation by algebraic elements of bounded degree in finite characteristic |

時間: | 2012-12-25 (Tue.) 10:00 - |

地點: | 數學所 617 研討室 (台大院區) |

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 Jarnik-Besicovitch theorem. In this talk we will give an analog of Baker and Schmidt's theorem in the fields of formal power series. |

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