Some studies on Klein forms and Eisenstein series = 클라인 형식과 아이젠슈타인 급수에 관한 연구

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In this thesis we discuss some modularity criterion for a product of Klein forms of the congruence subgroup $\Gamma_1(N)$ and some applications of Eisenstein series to the theta functions associated with certain quadratic forms. As an application of the Klein forms, we construct a basis of the space of modular forms for $\Gamma_1(13)$ of weight $2$. In the process we face with an interesting property about the coefficients of certain theta function from a quadratic form. We extend it to more general cases and prove it by applying Fricke involutions and Hecke operators to Eisenstein series and theta functions.
Advisors
Koo, Ja-Kyungresearcher구자경
Description
한국과학기술원 : 수리과학과,
Publisher
한국과학기술원
Issue Date
2012
Identifier
511836/325007  / 020085115
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2012.8, [ iii, 62 p. ]

Keywords

Modular form; Klein form; Eisenstein series; Quadratic form; 보형형식; 클라인 형식; 아이젠슈타인 급수; 이차형식; 씨타함수; Theta function

URI
http://hdl.handle.net/10203/181554
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=511836&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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