#### Arithmetic of Ramanujan's continued fractions and Hypergeometric series라마누잔 연분수와 초기하급수의 산술성

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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
Description
한국과학기술원 : 수리과학과,
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