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Successive Minima of Orders in Number Fields- [electronic resource]
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Successive Minima of Orders in Number Fields- [electronic resource]
Detailed Information
- 자료유형
- 학위논문파일 국외
- 최종처리일시
- 20240214100458
- ISBN
- 9798380413510
- DDC
- 510
- 서명/저자
- Successive Minima of Orders in Number Fields - [electronic resource]
- 발행사항
- [S.l.]: : Princeton University., 2023
- 발행사항
- Ann Arbor : : ProQuest Dissertations & Theses,, 2023
- 형태사항
- 1 online resource(179 p.)
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-04, Section: B.
- 주기사항
- Advisor: Bhargava, Manjul.
- 학위논문주기
- Thesis (Ph.D.)--Princeton University, 2023.
- 사용제한주기
- This item must not be sold to any third party vendors.
- 초록/해제
- 요약Orders in number fields provide interesting examples of lattices. We ask: what lattices arise from orders in number fields and how are they distributed? In the first chapter of this thesis, we prove that all nontrivial multiplicative constraints on successive minima of orders come from multiplication. Moreover, for infinitely many positive integers n (including all n 18), we explicitly determine all multiplicative constraints on successive minima of orders in degree n number fields. We also prove analogous results for scrollar invariants of curves. Now suppose 3 ≤ n ≤ 5 and let G ⊆ Sn. An order O of absolute discriminant ∆ in a degree n number field has n successive minima 1 = λ0 ≤ λ1 ≤ · · · ≤ λn−1. In the next three chapters, we compute for many G the distribution of the points (log∆ λ1, . . . , log∆ λn−1) ∈ Rn−1 as O ranges across orders in degree n fields with Galois group G as ∆ → ∞.
- 일반주제명
- Mathematics.
- 일반주제명
- Theoretical mathematics.
- 키워드
- Lattices arise
- 키워드
- Number theory
- 키워드
- Number fields
- 기타저자
- Princeton University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 85-04B.
- 기본자료저록
- Dissertation Abstract International
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798380413510
■035 ▼a(MiAaPQ)AAI30492597
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aVemulapalli, Sameera.
■24510▼aSuccessive Minima of Orders in Number Fields▼h[electronic resource]
■260 ▼a[S.l.]:▼bPrinceton University. ▼c2023
■260 1▼aAnn Arbor :▼bProQuest Dissertations & Theses, ▼c2023
■300 ▼a1 online resource(179 p.)
■500 ▼aSource: Dissertations Abstracts International, Volume: 85-04, Section: B.
■500 ▼aAdvisor: Bhargava, Manjul.
■5021 ▼aThesis (Ph.D.)--Princeton University, 2023.
■506 ▼aThis item must not be sold to any third party vendors.
■520 ▼aOrders in number fields provide interesting examples of lattices. We ask: what lattices arise from orders in number fields and how are they distributed? In the first chapter of this thesis, we prove that all nontrivial multiplicative constraints on successive minima of orders come from multiplication. Moreover, for infinitely many positive integers n (including all n 18), we explicitly determine all multiplicative constraints on successive minima of orders in degree n number fields. We also prove analogous results for scrollar invariants of curves. Now suppose 3 ≤ n ≤ 5 and let G ⊆ Sn. An order O of absolute discriminant ∆ in a degree n number field has n successive minima 1 = λ0 ≤ λ1 ≤ · · · ≤ λn−1. In the next three chapters, we compute for many G the distribution of the points (log∆ λ1, . . . , log∆ λn−1) ∈ Rn−1 as O ranges across orders in degree n fields with Galois group G as ∆ → ∞.
■590 ▼aSchool code: 0181.
■650 4▼aMathematics.
■650 4▼aTheoretical mathematics.
■653 ▼aGeometry of numbers
■653 ▼aLattices arise
■653 ▼aNumber theory
■653 ▼aNumber fields
■690 ▼a0405
■690 ▼a0642
■71020▼aPrinceton University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g85-04B.
■773 ▼tDissertation Abstract International
■790 ▼a0181
■791 ▼aPh.D.
■792 ▼a2023
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T16932438▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
■980 ▼a202402▼f2024
