請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/35935完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳其誠 | |
| dc.contributor.author | Po-Yi Huang | en |
| dc.contributor.author | 黃柏嶧 | zh_TW |
| dc.date.accessioned | 2021-06-13T07:48:27Z | - |
| dc.date.available | 2006-01-01 | |
| dc.date.copyright | 2005-07-26 | |
| dc.date.issued | 2005 | |
| dc.date.submitted | 2005-07-26 | |
| dc.identifier.citation | Noboru Aoki: Gross' Conjecture on the Special Values of
Abelian L-Functions at s=0, Commentarii Mathematici Universitatis Sancti Pauli 40(1991), p101-124. Noboru Aoki: On a refinement of a conjecture of Gross for cyclic extensions of global fields, Preprint, 2003 David Burns: On relations between derivatives of abelian $L$-functions at s=0, Preprint, 2002 Darmon, H.: Thaine's method for circular units and a conjecture of Gross, Canadian J. Math. 47(1995), 302-317. Benedict H. Gross: On the values of abelian L-functions at s=0, J.~Fac.~Sci.~Univ.~Tokyo Sect.~IA, Math. 35(1988), 177-197. Ronald L. Graham, Donald E. Knuth, Oren Patashnik: Concrete Mathematics: A Foundation for Computer SCience, Addison-Wesley Publishing Company, 1989. David R. Hayes: The refined p-adic abelian Stark conjecture in function fields, Invent.~Math. 94(1988), 505-527. Po-Yi Huang: Gross' Conjecture for Extensions Ramified over Four Points of P1, Preprint, 2004. Serge Lang: Algebraic Number Theory, Graduate Texts in Mathematics 110, Springer-Verlag, 1986. Joongul Lee: On Gross' Refined Class Number Formula for Elementary Abelian Extensions, Journal of Mathematical Sciences, University of Tokyo 4(1997), 373-383. Joongul Lee: Stickelberger elements for cyclic extensions and the order of vanishing of abelian L-functions at s=0, to appear in Comp. Math. Joongul Lee: On the refined class number formula for global function fields, Math. Res. Kett. 11 (2004), 283-289. I.B.S. Passa and I. R. Vermani: The associated graded ring of an integral group ring, Proc. Camb. Phil. Soc., 82(1997), 25-33. Michael Reid: Gross' Conjecture for extensions ramified over three points on P1, Journal of Mathematical Sciences, University of Tokyo 10 no. 1 (2003), 119-138. Ki-Seng Tan: On the special values of abelian L-functions, J.~Math.~Sci.~Univ.~Tokyo 1(1994), 305-319. Ki-Seng Tan: Refined theorems of the Birch and Swinnerton-Dyer type, Ann. Inst. Fourier 45,2(1995), 317-374. Ki-Seng Tan: A note on Stickelberger elements for cyclic p-ectension over global function fields of characteristic p, Math. Res. Kett. 11 (2004), 273-279. Yamagishi, M.: On a conjecture of Gross on special values of L-functions, Math. Z. 201(1989), 391-400. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/35935 | - |
| dc.description.abstract | The family of Stickelberger elements associated to
certain abelian extensions over global rational function fields is represented by a universal polynomial. This result is then used to prove a conjecture of Gross for these Stickelberger elements. Keywords: Stickelberger element, special values of abelian L-functions, Conjecture of Gross, Class numbers. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T07:48:27Z (GMT). No. of bitstreams: 1 ntu-94-D88221001-1.pdf: 317125 bytes, checksum: 5a9f6cdf015d3c74593e3ded0fd84eb0 (MD5) Previous issue date: 2005 | en |
| dc.description.tableofcontents | 1. Introduction .... 1
2. The Conjecture of Gross .... 4 2.1 The Regulator of Gross .... 4 2.2 The shifting of the basic datum .... 6 3. Example .... 9 3.1 Group ring result .... 9 3.2 An example of n=3 ... 11 4. Universal Polynomials ... 17 4.1 Some combinatorial formulae ... 17 4.2 Representable families ... 18 4.3 Computing theta ... 21 | |
| dc.language.iso | en | |
| dc.subject | 葛羅斯猜想 | zh_TW |
| dc.subject | special values of abelian L-functions | en |
| dc.subject | Class numbers | en |
| dc.subject | Conjecture of Gross | en |
| dc.subject | Stickelberger element | en |
| dc.title | 函數體上的葛羅斯猜想 | zh_TW |
| dc.title | Gross’ Conjecture on Rational Function Fields | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 93-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 紀文鎮,朱樺,王藹農,莊正良,夏良忠,謝春忠,余家富 | |
| dc.subject.keyword | 葛羅斯猜想, | zh_TW |
| dc.subject.keyword | Stickelberger element,special values of abelian L-functions,Conjecture of Gross,Class numbers, | en |
| dc.relation.page | 25 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2005-07-26 | |
| 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 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-94-1.pdf 未授權公開取用 | 309.69 kB | Adobe PDF |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。