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Convergence and Correlations of Coefficients of Cusp Forms
Convergence and Correlations of Coefficients of Cusp Forms
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211151449
- ISBN
- 9798382807225
- DDC
- 510
- 저자명
- Zubrilina, Nina.
- 서명/저자
- Convergence and Correlations of Coefficients of Cusp Forms
- 발행사항
- [Sl] : Princeton University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 132 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
- 주기사항
- Advisor: Sarnak, Peter.
- 학위논문주기
- Thesis (Ph.D.)--Princeton University, 2024.
- 초록/해제
- 요약In this thesis, we discuss aspects of lower-order statistical behavior of coefficients of GL2 automorphic forms. First, we establish two cases of recently observed correlation phenomena, referred to as "murmurations," between root numbers and L-function coefficients. The first is for the family of weight k modular cuspidal newforms. In that case, we show that averages of P-th Fourier coefficients correlated against the root number in a family of forms of conductor ∼ N converge to a function of P/N. In the second case (from joint work with Booker, Lee, Lowry-Duda, and Seymour-Howell), we prove an analogous result for the family of weight 0 level 1 Maass forms. In this case, additional averaging on P is required, and the answer is given by a measure evaluated on the interval of P-averaging. Finally, in joint work with Sarnak, we give new rates of convergence to the Plancherel measure for coefficients of holomorphic forms of weight 2 and bound the number of d-dimensional factors of the Jacobian of the modular curve.
- 일반주제명
- Mathematics
- 일반주제명
- Theoretical mathematics
- 키워드
- Correlation
- 키워드
- Elliptic curves
- 키워드
- Modular forms
- 키워드
- Murmurations
- 키워드
- Root number
- 기타저자
- Princeton University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 85-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520250211151449
■006m o d
■007cr#unu||||||||
■020 ▼a9798382807225
■035 ▼a(MiAaPQ)AAI31296664
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aZubrilina, Nina.
■24510▼aConvergence and Correlations of Coefficients of Cusp Forms
■260 ▼a[Sl]▼bPrinceton University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a132 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 85-12, Section: B.
■500 ▼aAdvisor: Sarnak, Peter.
■5021 ▼aThesis (Ph.D.)--Princeton University, 2024.
■520 ▼aIn this thesis, we discuss aspects of lower-order statistical behavior of coefficients of GL2 automorphic forms. First, we establish two cases of recently observed correlation phenomena, referred to as "murmurations," between root numbers and L-function coefficients. The first is for the family of weight k modular cuspidal newforms. In that case, we show that averages of P-th Fourier coefficients correlated against the root number in a family of forms of conductor ∼ N converge to a function of P/N. In the second case (from joint work with Booker, Lee, Lowry-Duda, and Seymour-Howell), we prove an analogous result for the family of weight 0 level 1 Maass forms. In this case, additional averaging on P is required, and the answer is given by a measure evaluated on the interval of P-averaging. Finally, in joint work with Sarnak, we give new rates of convergence to the Plancherel measure for coefficients of holomorphic forms of weight 2 and bound the number of d-dimensional factors of the Jacobian of the modular curve.
■590 ▼aSchool code: 0181.
■650 4▼aMathematics
■650 4▼aTheoretical mathematics
■653 ▼aCorrelation
■653 ▼aElliptic curves
■653 ▼aModular forms
■653 ▼aMurmurations
■653 ▼aRoot number
■653 ▼aStatistical distribution
■690 ▼a0405
■690 ▼a0642
■71020▼aPrinceton University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g85-12B.
■790 ▼a0181
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17161818▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
