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研究生: 田明弘
論文名稱: 函數體上的加強的六指數定理
Sharp Six exponentials Theorem in Finite characteristic
指導教授: 于靖
Jing Yu
口試委員:
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系
Department of Mathematics
論文出版年: 2004
畢業學年度: 92
語文別: 英文
論文頁數: 27
中文關鍵詞: 德林費模函數體指數函數六指數定理
外文關鍵詞: Drinfeld's module, function field, exponential function, six exponentials theorem
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  • 我們將研究函數體上的德林費指數函數。給定六個點,六指數定理證明了在適當的條件下,自然指數函數在這些點的取值至少有一個是超越元素。在數體的情況,加強的六指數定理改進了六指數定理。作為此定理的應用,五指數定理證明了給定五個適當的點,自然指數函數在這些點的取值必有超越元素。在這篇文章中,我們在函數體上導出了一個加強的六指數定理的類比。


    We study Drinfeld's exponential functions.The six exponentials theorem study the existence of transcendental elements among six suitably given exponential values, and the sharp six exponentials theorem improve this result to five. In this article, we deduce an analog of the sharp six exponentials theorem over function fields.

    Abstract………………………………………1 1. Introduction…………………………2 2. Main theorem and main result.….4 3. Transcendence argument………….11 4. Auxiliary lemma…………………..21 5. Proof of main result…………….23 Reference…………………………………..27

    1] Humphreys, E.: Linear Algebraic Groups. GTM 21, Springer-Verlag.
    2] Rosen, M.: Number Theory in Function Fields. GTM 210, Springer-Verlag.
    [3] Waldschmidt, M.: Diophantine Approximation on Linear Algebraic Groups.
    [4] Waldschmidt, M.: On the transcendence methods of Gelfond and Schneider in several variables. New advances in transdence theory (Durham, 1986), 375-398,Cambridge Univ.Press,Cambridge-New York,1988.
    [5] Yu, J.: Transcendence theory over function fields, Duke Math. J. 52 (1985), 517-527.
    [6] Yu, J.: A Six Exponentials Theorem in finite characteristic. Math. Ann. 272 (1985), 91-98.
    [7] Yu, J.: Transcedence and Drinfeld modules, Invent Math. 83(1986), 507-517.
    [8] Yu, J.: Transcedence and Drinfeld modules: several variables, Duke Math. J. 58 (1989), 559-575.
    [9] Yu, J.: Analytic homomorphisms into Drinfeld modules, Annals of Mathematics. 145 (1997), 215-233.

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