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研究生： 潘國隆
論文名稱： 多項式上的華林－哥德巴赫問題
ON POLYNOMIAL WARING--GOLDBACH PROBLEM
指導教授： 許志農
Hsu, Chih-Nung
學位類別： 碩士
Master
系所名稱： 數學系
Department of Mathematics
論文出版年： 1999
畢業學年度： 87
語文別： 英文
論文頁數： 60
中文關鍵詞： 圓法 、華林問題 、多項式上的華林－哥德巴赫問題
英文關鍵詞： circle method, Waring problem, polynomial Waring-Goldbach problem
論文種類： 學術論文
相關次數： 點閱：224  下載：0 
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    • 華林問題是去證明每一個自然數（足夠大）是一些有限範圍的正整數的ｄ次方的和；哥德巴赫問題是去證明每一個大過３的偶數是兩個質數的和，而每一個大過５的奇數是三個質數的和。所以，華林－哥德巴赫問題是探討把自然數展開成一些有限範圍的質數的ｄ次方（ｄ＞１）和的可能性。
    本篇論文中，我們研究把有限體上的多項式展開成一些質多項式的ｄ次方（ｄ＞１）和的問題。這個問題和古典的華林－哥德巴赫問題相似，所以我們稱之為『多項式上的華林－哥德巴赫問題』。

    section 1: Introduction section 2: Exponential sums of polynomial rings section 3: An estimation for sum involving the divisor function section 4: Hua's lemma for Fq[T] section 5: Vinogradov's mean value theorem for Fq[T] section 6: Weyl's inequality for polynomial Waring problem section 7: Hua's inequality for polynomial Waring problem section 8: The minor and major arcs in polynomial Waring-Goldbach problem section 9: The polynomial Waring-Goldbach singular series section 10:The polynomial Waring-Goldbach problem section 11:A theorem in additive theory of irreducible polynomials

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