簡易檢索 / 詳目顯示
| 研究生： |
杜炯熏 Chiung-Hsun Tu |
|---|---|
| 論文名稱： |
關於多項式因式函數的一個漸進公式 An asymptotic formula for polynomial divisor functions |
| 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： | 2005 |
| 畢業學年度： | 93 |
| 語文別： | 中文 |
| 論文頁數： | 15 |
| 中文關鍵詞： | 因式問題 、L函數 、函數體 |
| 英文關鍵詞： | Divisor Problem, L-functions, Function Fields |
| 論文種類： | 學術論文 |
| 相關次數： | 點閱：241 下載：13 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
我們探討一個跟古典林尼克漸近展開式很類似的有限體多項式因式函數展開式. 我們利用從多項式Brun-Titchmarsh定理得到的一些結果以及從多項式primitive character和所得的均值,使我們得到了一些結果.
In this paper, we explore an analogue of the classical Linnik's asymptotic expansion about polynomial divisor functions for polynomial rings over finite fields. Our method depends on the obtained result in the polynomial Brun-Titchmarsh theorem for polynomial divisor functions and an average of polynomial primitive character sums, we obtain a polynomial Linnik's asymptotic expansion.
[1]L. Carlitz,
The Arithmetic of Polynomials in a Galois Field,
American Journal of Mathematics
54 (1932), 39--50.
[2]K. Chandrasekharan,
Introduction To Analytic Number Theory,
Spring-Verlag (1968).
[3]H. Davenport,
Multiplicative Number Theory,
Springer-Verlag, GTM 74 (1980).
[4]G. W. Effinger and D. R. Hayes,
Additive Number Theory of Polynomials Over a Finite Field,
Clarendon Press Oxford (1991).
[5]Chih-Nung, Hsu,
Estimates for Coefficients of $L$-functions for Function Fields,
Finite Fields and Their Applications 5 (1999), 76--88.
[6]Chih-Nung, Hsu,
A Large Sieve Inequality for Rational Function Fields,
J. Number Theory 58 (1996), 267--287.
[7]Chih-Nung, Hsu,
A Polynomial Additive Divisor Promblem.
[8]R. Lidl and H. Niederreiter,
Finite Fields,
Encyclopedia of Mathematics and Its Applications Vol. 20, Cambridge University Press Cambridge UK (1997).
[9]Y. Motohashi,
An Asymptotic Formula in Theory of Numbers,
Acta Arith. 16 (1970), 255--264.
[10]P. Shiu,
A Brun-Titchmarsh theorem for multiplicative functions,
J. reine angew. Math. 313 (1980), 161--170.
