請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/51078完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳其誠(Ki-Seng Tan) | |
| dc.contributor.author | Da-wei Yang | en |
| dc.contributor.author | 楊大緯 | zh_TW |
| dc.date.accessioned | 2021-06-15T13:24:50Z | - |
| dc.date.available | 2016-07-04 | |
| dc.date.copyright | 2016-07-04 | |
| dc.date.issued | 2016 | |
| dc.date.submitted | 2016-06-09 | |
| dc.identifier.citation | [1] Lars V. Ahlfors, An Introduction to the Theory of Analytic Functions of One Complex Variable. Singapore: McGraw-Hill, 1979.
[2] Z.I. Borevich, I.R.Shafarevich, Number Theory. Academic Press, London,1966. [3] M. Ram Murty, Problems in Algebraic Number Theory, second edition.Springer, 2005. [4] William R.Wade, An introduction to Analysis. United States of America:Pearson Education, Inc. ,2010. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/51078 | - |
| dc.description.abstract | 我們使用Weierstrass factorization theorem 去求出某一類由多項式定義出的無窮連乘積之收斂值。然後我們應用這個結果可以求出一些無窮級數和定積分的封閉形式。另一方面，我們求出一些狄利克雷級數的收斂值(對某些狄利克雷特徵X )。更進一步，我們推導出一個新的類數公式(其中d 是正奇數,square free,且大於3) | zh_TW |
| dc.description.abstract | We use Weierstrass factorization theorem to evaluate the infinite product defined by some polynomials.Then we apply the result to express some infinite series and definite integral in closed form. On the other hand, we find out the value of Dirichlet L-function for some Dirichlet character
X .Moreover, we deduce a new class number formula (where d is positive integer, square free, and greater than 3) | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T13:24:50Z (GMT). No. of bitstreams: 1 ntu-105-R01221018-1.pdf: 1299993 bytes, checksum: 5cbf53b8487fb5ade0b0202563afbfdd (MD5) Previous issue date: 2016 | en |
| dc.description.tableofcontents | 1.INTRODUCTION(p1)
2.THE INFINITE PRODUCT(p1) 3.THE EVALUATION OF SOME SPECIAL INFINITE SERIES(p3) 4.THE EVALUATION OF L(X,s) FOR SOME SPECIAL CHARACTER X(p5) 5.A FORMULA FOR CLASS NUMBERS OF QUADRATIC FIELDS(p9) 6.FURTHER RESULTS(p12) 7.REFERENCES(p16) | |
| dc.language.iso | en | |
| dc.subject | 狄利克雷級數 | zh_TW |
| dc.subject | 無窮乘積 | zh_TW |
| dc.subject | 多項式 | zh_TW |
| dc.subject | 無窮級數 | zh_TW |
| dc.subject | Zeta 函數 | zh_TW |
| dc.subject | 勒讓德符號 | zh_TW |
| dc.subject | 類數公式 | zh_TW |
| dc.subject | 無窮乘積 | zh_TW |
| dc.subject | 多項式 | zh_TW |
| dc.subject | 無窮級數 | zh_TW |
| dc.subject | Zeta 函數 | zh_TW |
| dc.subject | 狄利克雷級數 | zh_TW |
| dc.subject | 勒讓德符號 | zh_TW |
| dc.subject | 類數公式 | zh_TW |
| dc.subject | infinite product | en |
| dc.subject | class number formula | en |
| dc.subject | polynomial | en |
| dc.subject | infinite series | en |
| dc.subject | zeta function | en |
| dc.subject | Dirichlet L-series | en |
| dc.subject | Legendre symbol | en |
| dc.subject | class number formula | en |
| dc.subject | infinite product | en |
| dc.subject | polynomial | en |
| dc.subject | infinite series | en |
| dc.subject | zeta function | en |
| dc.subject | Dirichlet L-series | en |
| dc.subject | Legendre symbol | en |
| dc.title | 無窮乘積、狄利克雷級數和勒讓德符號 | zh_TW |
| dc.title | Infinite Product, Dirichlet L-series, and Legendre symbol | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 王藹農(Ai-Nung Wang),紀文鎮(Wen-Chen Chi) | |
| dc.subject.keyword | 無窮乘積,多項式,無窮級數,Zeta 函數,狄利克雷級數,勒讓德符號,類數公式, | zh_TW |
| dc.subject.keyword | infinite product,polynomial,infinite series,zeta function,Dirichlet L-series,Legendre symbol,class number formula, | en |
| dc.relation.page | 16 | |
| dc.identifier.doi | 10.6342/NTU201600317 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2016-06-11 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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