DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 임보해 | - |
dc.contributor.author | Lee, Wonwoong | - |
dc.contributor.author | 이원웅 | - |
dc.date.accessioned | 2024-07-26T19:31:02Z | - |
dc.date.available | 2024-07-26T19:31:02Z | - |
dc.date.issued | 2023 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=1047418&flag=dissertation | en_US |
dc.identifier.uri | http://hdl.handle.net/10203/320991 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수리과학과, 2023.8,[iii, 82 p. :] | - |
dc.description.abstract | We study several arithmetic properties of automorphic forms for certain Fuchsian groups including $\Gamma_0^+(2)$ and $\Gamma_0^+(3)$. The result includes the algebraic independence of the values of the Eisenstein series for the arithmetic Hecke group and the investigation of the common zeros and the multiplicities of zeros of quasi-modular forms. More precisely, we prove that for any $\alpha$ in the upper half-plane, at least three of the numbers $e^{2\pi i \alpha}, E_{2,m}(\alpha), E_{4,m}(\alpha), E_{6,m}(\alpha)$ are algebraically independent over $\mathbb Q$, which is an extension of Nesterenko's result. As its application, we study the zeros of quasi-modular forms of depth 1 for $\Gamma_0^+(N)$, for $N=2,3$. In addition, we give the formula of the non-holomorphic Eisenstein series for certain Fuchsian groups whose elliptic points coincide with the quadratic class group and provide an explicit basis for the space of polyharmonic Maass forms for these groups. | - |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | 모듈러 형식▼a준-모듈러 형식▼a프리케군▼a헤케 삼각군▼a비정칙 아이젠슈타인 급수▼a다중조화 마스 형식 | - |
dc.subject | Modular forms▼aQuasi-modular forms▼aFricke groups▼aHecke triangle groups▼aNon-holomorphic Eisenstein series▼aPolyharmonic Maass forms | - |
dc.title | Arithmetic of automorphic forms for certain Fuchsian groups including $\Gamma_0^+(2)$ and $\Gamma_0^+(3)$ | - |
dc.title.alternative | $\Gamma_0^+(2)$와 $\Gamma_0^+(3)$를 포함하는 특정 푹스군에 관한 보형 형식의 산술 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 325007 | - |
dc.description.department | 한국과학기술원 :수리과학과, | - |
dc.contributor.alternativeauthor | Im, Bo-Hae | - |
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