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Distribution of the Successive Minima of the Petersson Norm on Cusp Forms
Distribution of the Successive Minima of the Petersson Norm on Cusp Forms
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211150943
- ISBN
- 9798382829968
- DDC
- 510
- 서명/저자
- Distribution of the Successive Minima of the Petersson Norm on Cusp Forms
- 발행사항
- [Sl] : University of Pennsylvania, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 61 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
- 주기사항
- Advisor: Chinburg, Ted.
- 학위논문주기
- Thesis (Ph.D.)--University of Pennsylvania, 2024.
- 초록/해제
- 요약Given an arithmetic variety \uD835\uDCE7 and a hermitian line bundle \uD835\uDCDB , the arithmetic Hilbert-Samuel theorem describes the asymptotic behavior of the co-volumes of the lattices H0 (\uD835\uDCE7 ,\uD835\uDCDB ⊗k ) in the normed spaces H0 ( \uD835\uDCE7 , \uD835\uDCDB ⊗k )⊗ℝ as k → ∞. Using his work on quasi-filtered graded algebras, Chen proved a variant of the arithmetic Hilbert-Samuel theorem which studies the asymptotic behavior of the successive minima of the lattices above. Chen's theorem, however, requires that the metric on \uD835\uDCDB is continuous, and hence does not apply to automorphic vector bundles for which the natural metrics are often singular. In this thesis, we discuss a version of Chen's theorem for the line bundle of modular forms for a finite index subgroup Γ ⊆ PSL2(ℤ) endowed with the logarithmically singular Petersson metric. This generalizes work of Chinburg, Guignard, and Soule addressing the case Γ = PSL2(ℤ).
- 일반주제명
- Mathematics
- 일반주제명
- Applied mathematics
- 키워드
- Arakelov theory
- 키워드
- Number theory
- 키워드
- Petersson metric
- 기타저자
- University of Pennsylvania Mathematics
- 기본자료저록
- Dissertations Abstracts International. 85-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798382829968
■035 ▼a(MiAaPQ)AAI30992108
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aPurohit, Souparna.
■24510▼aDistribution of the Successive Minima of the Petersson Norm on Cusp Forms
■260 ▼a[Sl]▼bUniversity of Pennsylvania▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a61 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 85-12, Section: B.
■500 ▼aAdvisor: Chinburg, Ted.
■5021 ▼aThesis (Ph.D.)--University of Pennsylvania, 2024.
■520 ▼aGiven an arithmetic variety \uD835\uDCE7 and a hermitian line bundle \uD835\uDCDB , the arithmetic Hilbert-Samuel theorem describes the asymptotic behavior of the co-volumes of the lattices H0 (\uD835\uDCE7 ,\uD835\uDCDB ⊗k ) in the normed spaces H0 ( \uD835\uDCE7 , \uD835\uDCDB ⊗k )⊗ℝ as k → ∞. Using his work on quasi-filtered graded algebras, Chen proved a variant of the arithmetic Hilbert-Samuel theorem which studies the asymptotic behavior of the successive minima of the lattices above. Chen's theorem, however, requires that the metric on \uD835\uDCDB is continuous, and hence does not apply to automorphic vector bundles for which the natural metrics are often singular. In this thesis, we discuss a version of Chen's theorem for the line bundle of modular forms for a finite index subgroup Γ ⊆ PSL2(ℤ) endowed with the logarithmically singular Petersson metric. This generalizes work of Chinburg, Guignard, and Soule addressing the case Γ = PSL2(ℤ).
■590 ▼aSchool code: 0175.
■650 4▼aMathematics
■650 4▼aApplied mathematics
■653 ▼aArakelov theory
■653 ▼aArithmetic geometry
■653 ▼aNumber theory
■653 ▼aAsymptotic behavior
■653 ▼aPetersson metric
■690 ▼a0405
■690 ▼a0364
■71020▼aUniversity of Pennsylvania▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g85-12B.
■790 ▼a0175
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17160253▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
