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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/2452完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 謝春忠(Chun-Chung Hsieh) | |
| dc.contributor.author | Zhong Tang Wu | en |
| dc.contributor.author | 吳宗堂 | zh_TW |
| dc.date.accessioned | 2021-05-13T06:40:24Z | - |
| dc.date.available | 2017-07-28 | |
| dc.date.available | 2021-05-13T06:40:24Z | - |
| dc.date.copyright | 2017-07-28 | |
| dc.date.issued | 2017 | |
| dc.date.submitted | 2017-07-25 | |
| dc.identifier.citation | [1] Brning Jochen and Seeley Robert, The resolvent expansion for second order regular singular operators, Journal of functional analysis,vol.73,no.2,p.369-p.429,1987,
Elsevier [2] Lesch Matthias, Determinants of Regular Singular Sturm-Liouville Operators, Mathematische Nachrichten, vol.194, no.1, p.139-p.170, 1998, Wiley Online Library [3] Yoshida Masaaki, Hypergeometric functions, my love: modular interpretations of conguration spaces, 2013, Springer Science& Business Media [4] Mimachi Katsuhisa and Yoshida Masaaki, Intersection numbers of twisted cycles and the correlation functions of the conformal field theory, Communications in mathematical physics, vol.234, no.2, p.339-p.358, 2003, Springer [5] Ichikawa Takashi, Teichmller groupoids and Galois action, Journal fur die Reine und Angewandte Mathematik, vol.559, p.95-p.114,2 003, Walter de Gruyter Berlin New York [6] Ichikawa Takashi, Teichmller groupoids,and monodromy in conformal field theory, Communications in mathematical physics, vol.246, no.1, p.1-p.18, 2004, Springer [7] Brning Jochen and Seeley Robert Regular singular asymptotics, Advances in mathematics, vol.58, no.2, p.133-p.148,1985,Elsevier [8] Brning Jochen, Heat equation asymptotics for singular Sturm-Liouville operators, Mathematische Annalen, vol.268, no.2, p.173-p.196, 1984, Springer [9] Umehara Masaaki and Yamada Kotaro and others, Metrics of constant curvature 1 with three conical singularities on the 2-sphere, Illinois Journal of Mathematics, vol.44, no.1, p.72-p.94, 2000, University of Illinois at Urbana-Champaign,Department of Mathematics [10] Kraus Daniela and Roth Oliver and Sugawa Toshiyuki, Metrics with conical singularities on the sphere and sharp extensions of the theorems of Landau and Schottky, Mathematische Zeitschrift,vol.267,no.3,p.851-p.868, 2011, Springer [11] BruceC.Berndt, Ramanujans Notebooks,Part2, 1989, Springer NewYork [12] BruceC.Berndt,S.Bhargava and Frank G.Garvan, Ramanujan's theories of elliptic functions to alternative bases, Trans.Amer.Math.Soc.347,4163-4244,1995, American Mathematical Society. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/2452 | - |
| dc.description.abstract | 本文研究高斯超幾何方程的施圖姆-劉維爾形式及其Zeta 行列式.基於Lesch 給出以wronskian 表示正則奇異施圖姆-劉維爾算子之Zeta 行列式的公式,以及拉馬努金的某項公式,便得出本文的主要結果: 超幾何方程之施圖姆-劉維爾形式的Zeta 行列式之closed form. | zh_TW |
| dc.description.abstract | In the thesis, the eignevalue probelm of the Hypergeometric equation(for short: HGE or E(a,b,c)) is discussed. There are three parts in this thesis.First of all, I introduce some heuristic backgrounds and motivations of the eigenvalue problem of HGE. The second part is a survey about the theory of the HGE. Finally, based on Lesch’s formula of zeta determinant of Regular Singular Sturm-Liouville Operators, I calculate the zeta determinant with repect to the Sturm-Liouville form of HGE operator on a closed interval, by using Ramanujan's identities. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-13T06:40:24Z (GMT). No. of bitstreams: 1 ntu-106-R02221007-1.pdf: 813721 bytes, checksum: f41593abd26e5d80b80417d175fceabb (MD5) Previous issue date: 2017 | en |
| dc.description.tableofcontents | 口試委員會審定書……………………………………………………………… #
誌謝………………………………………………………………………………. i 中文摘要………………………………………………………………………… ii Abstract……………………………..…………………………………………… iii 第一章 Introduction…………………………………………………………………..1 1.1 Motivation and main results…...…………………………………………… 1 1.2 Heat Kernel and Mellin Transform in the Case of Riemann Zeta………….. 4 1.3 Some Backgrounds………………………………………..…………………6 第二章A Survey of the Hypergeometric Equation……………..…………………. 8 2.1 Hypergeomteric Series.…………………………………..……………….…8 2.2 Hypergeomteric Equation..……………..………………..……………….…8 2.3 Integral representation of Hypergeomteric series.…….....……………….…9 2.4 Projective Equivalence implies Sturm-Liouville form of Hypergeomteric equation..……………..………………..……………….…..……………..……..9 2.5 Schwarz derivative of Schwarz map..……. ....………....………………….10 第三章 Calculation of the Zeta Determinant….. ……………………….…………12 第四章 Appendix…………………………………………..………………………15 4.1 Laplacian in polar coordinates of half plane and Disk.…………………….15 4.2 Eigenproblem of Laplacian implies hypergeometric..…………………..….15 參考文獻…………………………………………………………………….…… 18 | |
| dc.language.iso | en | |
| dc.subject | Zeta 行列式 | zh_TW |
| dc.subject | 高斯超幾何方程 | zh_TW |
| dc.subject | closed form | zh_TW |
| dc.subject | 拉馬努金公式 | zh_TW |
| dc.subject | 正則奇異施圖姆-劉維爾算子 | zh_TW |
| dc.subject | Regular Singular Sturm-Liouville operators. | en |
| dc.subject | Zeta determinant | en |
| dc.subject | Sturm-Liouville form | en |
| dc.subject | Hypergeometric equation | en |
| dc.title | 超幾何算子之 ZETA 行列式 | zh_TW |
| dc.title | ZETA Determinant of Hypergeomertic Equation via
Ramanujan’s Identity | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 105-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.coadvisor | 陳其誠(Ki-Seng Tan) | |
| dc.contributor.oralexamcommittee | 王藹農(Ai-Nung Wang),梁惠禎(Fei-tsen Liang) | |
| dc.subject.keyword | 高斯超幾何方程,Zeta 行列式,正則奇異施圖姆-劉維爾算子,拉馬努金公式,closed form, | zh_TW |
| dc.subject.keyword | Hypergeometric equation,Sturm-Liouville form,Zeta determinant,Regular Singular Sturm-Liouville operators., | en |
| dc.relation.page | 19 | |
| dc.identifier.doi | 10.6342/NTU201701882 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2017-07-25 | |
| 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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