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研究生： 連城
論文名稱： AN OVERVIEW OF ZETA FUNCTIONS ON HYPERSURFACES OVER FINITE FIELDS AND DWORK'S THEOREM
AN OVERVIEW OF ZETA FUNCTIONS ON HYPERSURFACES OVER FINITE FIELDS AND DWORK'S THEOREM
指導教授： 夏良忠
學位類別： 碩士
Master
系所名稱： 數學系
Department of Mathematics
論文出版年： 2014
畢業學年度： 102
語文別： 中文
論文頁數： 24
英文關鍵詞： finite fields, p-adic numbers, Dwork's Theorem, Newton polygon, Weierstrass Preparation Theorem
論文種類： 學術論文
相關次數： 點閱：102  下載：16 
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    • We study the Hasse Weil zeta function associated to
    a hypersurface of dimension n over finite fi eld. The main goal is to give an overview of the proof of Dwork's Theorem. The main ingredients are p-adic analysis, linear algebra, and Weierstrass Preparation Theorem

    1. Introduction 3 2. Preliminaries 3 3. p-adic number and p-adic power series 5 4. Counting the set of rational points 8 5. Linear maps on the vector space of power series 12 6. Newton polygon and Weierstrass Preparation Theorem 17 7. The end of the proof 21 References 24

    [1] Neal Koblitz, p-adic Numbers, p-adic Analysis, and Zeta-Functions, (1984),10-
    120.
    [2] Kenneth Ireland and Michael Rosen, A Classical Introduction to Modern Num-
    ber Theory, (1972), 151-166.
    [3] John B. Fraleigh, A First Course in Abstract Algebra, (2003), 457-463.
    [4] Walter Rudin, Principles of Mathematical Analysis(third edition), (1976), 47-
    53.

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