DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Koo, Ja-Kyung | - |
dc.contributor.advisor | 구자경 | - |
dc.contributor.author | Park, Yoon-Kyung | - |
dc.contributor.author | 박윤경 | - |
dc.date.accessioned | 2011-12-14T04:40:20Z | - |
dc.date.available | 2011-12-14T04:40:20Z | - |
dc.date.issued | 2008 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=303597&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/41906 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수리과학과, 2008. 8., [ iv, 57 p. ] | - |
dc.description.abstract | In this thesis we study three topics. First we treat certain Ramanujan`s continued fractions. One of the famous continued fractions which were studied by Ramanujan is the Rogers-Ramanujan continued fraction $R(\tau)$ . Through the works of Gee and Honesbeek([15]), Duke([13]), Cais and Conrad([2]), we see that there are some interesting facts about modularity of $R(\tau)$ , its modular equations and application to the construction of ray class fields. So we will investigate these topics with other Ramanujan`s continued fractions such as $v(\tau)$ and $C(\tau)$ . Second we will treat the growth of the coefficients of the modular equations for a modular function. P. Cohen first found some growth condition of the coefficients of modular equation for $j(\tau)$ ([7]) and Cais and Conrad showed that the ratio of the logarithmic heights of $j(\tau)$ and $j_5 (\tau)$ , which is the Hauptmodul of $\Gamma(5)$ , goes to the group index $[\overline {\Gamma(1)}: \overline {\Gamma(5)}]$ as n approaches $\infty$ . And we extend it to the case of somewhat general Hauptmoduln. Finally we introduce some identities of basic hypergeometric series and prove them. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | 보형형식 | - |
dc.subject | 연분수 | - |
dc.subject | 라마누잔 | - |
dc.subject | 초기하급수 | - |
dc.subject | modular form | - |
dc.subject | continued fraction | - |
dc.subject | Ramanujan | - |
dc.subject | hypergeometric series | - |
dc.subject | 보형형식 | - |
dc.subject | 연분수 | - |
dc.subject | 라마누잔 | - |
dc.subject | 초기하급수 | - |
dc.subject | modular form | - |
dc.subject | continued fraction | - |
dc.subject | Ramanujan | - |
dc.subject | hypergeometric series | - |
dc.title | Arithmetic of Ramanujan's continued fractions and Hypergeometric series | - |
dc.title.alternative | 라마누잔 연분수와 초기하급수의 산술성 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 303597/325007 | - |
dc.description.department | 한국과학기술원 : 수리과학과, | - |
dc.identifier.uid | 020035122 | - |
dc.contributor.localauthor | Koo, Ja-Kyung | - |
dc.contributor.localauthor | 구자경 | - |
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