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p-Adic L-Functions for P-Ordinary Hida Families on Unitary Groups
p-Adic L-Functions for P-Ordinary Hida Families on Unitary Groups
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103056
- ISBN
- 9798314846247
- DDC
- 510
- 저자명
- Marcil, David.
- 서명/저자
- p-Adic L-Functions for P-Ordinary Hida Families on Unitary Groups
- 발행사항
- [Sl] : Columbia University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 246 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-11, Section: B.
- 주기사항
- Advisor: Harris, Michael.
- 학위논문주기
- Thesis (Ph.D.)--Columbia University, 2025.
- 초록/해제
- 요약We construct a p-adic L-function for P-ordinary Hida families of cuspidal automorphic representations on a unitary group G. The main new idea of our work is to incorporate the theory of Schneider-Zink types for the Levi quotient of P, to allow for the possibility of higher ramification at primes dividing p, into the study of (p-adic) modular forms and automorphic representations on G. For instance, we describe the local structure of such a P-ordinary automorphic representation π at p using these types, allowing us to analyze the geometry of P-ordinary Hida families. Furthermore, these types play a crucial role in the construction of certain Siegel Eisenstein series designed to be compatible with such Hida families in two specific ways : Their Fourier coefficients can be p-adically interpolated into a p-adic Eisenstein measure on d + 1 variables and, via the doubling method of Garrett and Piatetski-Shapiro-Rallis, the corresponding zeta integrals yield special values of standard L-functions. Here, d is the rank of the Levi quotient of P. Lastly, the doubling method is reinterpreted algebraically as a pairing between modular forms on G, whose nebentype are types, and viewed as the evaluation of our p-adic L-function at classical points of a P-ordinary Hida family.
- 일반주제명
- Mathematics
- 일반주제명
- Theoretical mathematics
- 일반주제명
- Applied mathematics
- 키워드
- Iwasawa theory
- 키워드
- Number theory
- 기타저자
- Columbia University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 86-11B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■007cr#unu||||||||
■020 ▼a9798314846247
■035 ▼a(MiAaPQ)AAI31932695
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aMarcil, David.
■24510▼ap-Adic L-Functions for P-Ordinary Hida Families on Unitary Groups
■260 ▼a[Sl]▼bColumbia University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a246 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-11, Section: B.
■500 ▼aAdvisor: Harris, Michael.
■5021 ▼aThesis (Ph.D.)--Columbia University, 2025.
■520 ▼aWe construct a p-adic L-function for P-ordinary Hida families of cuspidal automorphic representations on a unitary group G. The main new idea of our work is to incorporate the theory of Schneider-Zink types for the Levi quotient of P, to allow for the possibility of higher ramification at primes dividing p, into the study of (p-adic) modular forms and automorphic representations on G. For instance, we describe the local structure of such a P-ordinary automorphic representation π at p using these types, allowing us to analyze the geometry of P-ordinary Hida families. Furthermore, these types play a crucial role in the construction of certain Siegel Eisenstein series designed to be compatible with such Hida families in two specific ways : Their Fourier coefficients can be p-adically interpolated into a p-adic Eisenstein measure on d + 1 variables and, via the doubling method of Garrett and Piatetski-Shapiro-Rallis, the corresponding zeta integrals yield special values of standard L-functions. Here, d is the rank of the Levi quotient of P. Lastly, the doubling method is reinterpreted algebraically as a pairing between modular forms on G, whose nebentype are types, and viewed as the evaluation of our p-adic L-function at classical points of a P-ordinary Hida family.
■590 ▼aSchool code: 0054.
■650 4▼aMathematics
■650 4▼aTheoretical mathematics
■650 4▼aApplied mathematics
■653 ▼aAutomorphic representations
■653 ▼aIwasawa theory
■653 ▼aNumber theory
■653 ▼aSiegel Eisenstein series
■690 ▼a0405
■690 ▼a0642
■690 ▼a0364
■71020▼aColumbia University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g86-11B.
■790 ▼a0054
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17356889▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
