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The Geometry of Secondary Terms in Arithmetic Statistics
The Geometry of Secondary Terms in Arithmetic Statistics
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103532
- ISBN
- 9798280712539
- DDC
- 510
- 저자명
- Kural, Michael.
- 서명/저자
- The Geometry of Secondary Terms in Arithmetic Statistics
- 발행사항
- [Sl] : Harvard University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 156 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
- 주기사항
- Advisor: Wood, Melanie Matchett.
- 학위논문주기
- Thesis (Ph.D.)--Harvard University, 2025.
- 초록/해제
- 요약In this thesis, we prove the existence of a secondary term for the count of cubic extensions of the function field Fq(t) of fixed absolute norm of discriminant. We show that the number of cubic extensions with absolute norm of discriminant equal to q2N is c1q2N − ci 2q5N/3 + Oε (q (3/2+ε)N) , where c1 and ci2 are explicit constants and ci2 only depends on N (mod 3). This builds on the work of Bhargava-Shankar-Tsimerman and Taniguchi-Thorne, who proved the existence of a secondary term for the count of cubic extensions of Q with bounded discriminant. Our approach uses a parametrization of Miranda and Casnati-Ekedahl, which can be seen as a geometric version of the classical parametrization by binary cubic forms used by Davenport-Heilbronn. This allows us to count and sieve for smooth curves embedded in Hirzebruch surfaces, in the same spirit as Zhao and Gunther.
- 일반주제명
- Mathematics
- 일반주제명
- Statistics
- 일반주제명
- Applied mathematics
- 키워드
- Discriminant
- 키워드
- Parametrization
- 키워드
- Cubic extensions
- 기타저자
- Harvard University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 86-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798280712539
■035 ▼a(MiAaPQ)AAI32040113
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aKural, Michael.▼0(orcid)0009-0004-4026-1616
■24510▼aThe Geometry of Secondary Terms in Arithmetic Statistics
■260 ▼a[Sl]▼bHarvard University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a156 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-12, Section: B.
■500 ▼aAdvisor: Wood, Melanie Matchett.
■5021 ▼aThesis (Ph.D.)--Harvard University, 2025.
■520 ▼aIn this thesis, we prove the existence of a secondary term for the count of cubic extensions of the function field Fq(t) of fixed absolute norm of discriminant. We show that the number of cubic extensions with absolute norm of discriminant equal to q2N is c1q2N − ci 2q5N/3 + Oε (q (3/2+ε)N) , where c1 and ci2 are explicit constants and ci2 only depends on N (mod 3). This builds on the work of Bhargava-Shankar-Tsimerman and Taniguchi-Thorne, who proved the existence of a secondary term for the count of cubic extensions of Q with bounded discriminant. Our approach uses a parametrization of Miranda and Casnati-Ekedahl, which can be seen as a geometric version of the classical parametrization by binary cubic forms used by Davenport-Heilbronn. This allows us to count and sieve for smooth curves embedded in Hirzebruch surfaces, in the same spirit as Zhao and Gunther.
■590 ▼aSchool code: 0084.
■650 4▼aMathematics
■650 4▼aStatistics
■650 4▼aApplied mathematics
■653 ▼aDiscriminant
■653 ▼aParametrization
■653 ▼aBinary cubic forms
■653 ▼aCubic extensions
■690 ▼a0405
■690 ▼a0463
■690 ▼a0364
■71020▼aHarvard University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g86-12B.
■790 ▼a0084
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17357583▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
