#### Arithmetic of Ramanujan's continued fractions and Hypergeometric series = 라마누잔 연분수와 초기하급수의 산술성

In this thesis we study three topics. First we treat certain Ramanujans 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 Ramanujans 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.
Koo, Ja-Kyungresearcher구자경researcher
Publisher
한국과학기술원
Issue Date
2008
Identifier
303597/325007  / 020035122
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2008. 8., [ iv, 57 p. ]

Keywords

보형형식; 연분수; 라마누잔; 초기하급수; modular form; continued fraction; Ramanujan; hypergeometric series; 보형형식; 연분수; 라마누잔; 초기하급수; modular form; continued fraction; Ramanujan; hypergeometric series

URI
http://hdl.handle.net/10203/41906
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=303597&flag=t
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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