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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:238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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