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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 謝銘倫 | zh_TW |
| dc.contributor.advisor | Ming-Lun Hsieh | en |
| dc.contributor.author | 姚皓勻 | zh_TW |
| dc.contributor.author | Hao-Yun Yao | en |
| dc.date.accessioned | 2023-08-01T16:28:54Z | - |
| dc.date.available | 2023-11-09 | - |
| dc.date.copyright | 2023-08-01 | - |
| dc.date.issued | 2023 | - |
| dc.date.submitted | 2023-07-08 | - |
| dc.identifier.citation | [God58] R. Godement. Topologie algébrique et théorie des faisceaux. Hermann, 1958.
[Gro61] Alexander Grothendieck. “Éléments de géométrie algébrique : III. Étude cohomologique des faisceaux cohérents, Première partie”. fr. In: Publications Mathématiques de l’IHÉS 11 (1961), pp. 5–167. [Tat68] John Tate. “Residues of differentials on curves”. en. In: Annales scientifiques de l’École Normale Supérieure Ser. 4, 1.1 (1968), pp. 149–159. [JL70] H. Jacquet and R. P. Langlands. Automorphic forms on GL(2). Lecture Notes in Mathematics, Vol. 114. Springer-Verlag, 1970. [Jac72] H. Jacquet. Automorphic forms on GL(2). Part II. Lecture Notes in Mathematics, Vol. 278. Springer-Verlag, 1972. [Cas73] William Casselman. “On Some Results of Atkin and Lehner.” In: Mathematische Annalen 201 (1973), pp. 301–314. [Tat79] John Tate. “Number theoretic background”. In: Automorphic forms, representations and L-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part. Vol. 2. 1979, pp. 3–26. [Fos81] O. Foster. Lectures on Riemann Surfaces. Springer, 1981. [Wal85] J.-L. Waldspurger. “Quelques propriétés arithmétiques de certaines formes automorphes sur GL(2)”. fr. In: Compositio Mathematica 54.2 (1985), pp. 121–171. [Har89] Michael Harris. “Functorial Properties of Toroidal Compactifications of Locally Symmetric Varieties”. In: Proceedings of the London Mathematical Society s3-59.1 (1989), pp. 1–22. [Clo90] Laurent Clozel. “Motifs et formes automorphes: applications du principe de fonctorialité”. In: Automorphic forms, Shimura varieties, and L-functions 1 (1990), pp. 77–159. [Har90a] Michael Harris. “Automorphic forms of B-cohomology type as coherent cohomology classes”. In: Journal of Differential Geometry 32.1 (1990), pp. 1–63. [Har90b] Michael Harris. “Period invariants of Hilbert modular forms, I: Trilinear differential operators and L-functions”. In: Cohomology of Arithmetic Groups and Automorphic Forms. Ed. by Jean-Pierre Labesse and Joachim Schwermer. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990, pp. 155–202. isbn: 978-3-540-46876-9. [Ram01] Dinakar Ramakrishnan. Modularity of solvable Artin representations of GO(4)-type. 2001. arXiv:math/0102231. [Voi02] Claire Voisin. Hodge Theory and Complex Algebraic Geometry I. Cambridge University Press, 2002. [Kri03] M. Krishnamurthy. “The Asai transfer to GL4 via the Langlands-Shahidi method”. In: International Mathematics Research Notices 2003.41 (2003), pp. 2221–2254. [Kab04] Anthony C. Kable. “Asai L-Functions and Jacquet’s Conjecture”. In: American Journal of Mathematics 126.4 (2004), pp. 789–820. issn: 00029327, 10806377. [Bla06] Don Blasius. “Hilbert modular forms and the Ramanujan conjecture”. In: Noncommutative Geometry and Number Theory: Where Arithmetic meets Geometry and Physics. Ed. by Caterina Consani and Matilde Marcolli. Wiesbaden: Vieweg, 2006, pp. 35–56. isbn: 978-3-8348-0352-8. [Ser12] Jean-Pierre Serre. Algebraic groups and class fields. Springer Science & Business Media, 2012. [Su18] Jun Su. Coherent cohomology of Shimura varieties and automorphic forms. 2018. arXiv: 1810.12056 [math.NT]. [CCI20] Shih-Yu Chen, Yao Cheng, and Isao Ishikawa. “Gamma factors for the Asai representation of GL2”. In: Journal of Number Theory 209 (2020), pp. 83–146. issn: 0022-314X. [Che21] Shih-Yu Chen. “Algebraicity of the central critical values of twisted triple product L-functions”. In: Annales mathématiques du Québec (2021), pp. 1–40. [Che23] Shih-Yu Chen. Period relations between the Betti-Whittaker periods for GLn under duality. 2023. arXiv:2302.04714 [math.NT]. [JS77] H. Jacquet and J. Shalika. “A non-vanishing theorem for zeta functions of GLn”. In: Invent. Math. 38.1 (1976/77), pp. 1–16. issn: 0020-9910. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/88027 | - |
| dc.description.abstract | 本論文主要證明了實二次擴張的既約尖點動原表現誘導出的淺井L函數臨界值的 代數性。透過比較 Harris 的 d-bar 上同調理論給出的有理結構以及新形式給出的有理結構所得出的週期，我們利用Rankin-Selberg積分的代數性證明了極右臨界值的代數性。在一些正規限制，其餘臨界值的代數性遂出。 | zh_TW |
| dc.description.abstract | In this thesis, we prove the algebraicity of critical values for Asai L-function associated to an irreducible cuspidal cohomological representation over a real quadratic field. We define associated periods by comparing the rational structure of d-bar cohomology on Hilbert modular surfaces from the theory developed by Harris with the one from the theory of newforms. The algebraicity of rightmost critical values is then given by the one of twisted Rankin-Selberg integrals. Under some regularity condition, the algebraicity for other critical values follows. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-08-01T16:28:54Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2023-08-01T16:28:54Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 目錄
致謝 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i 摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Abstract ........................................................ iii 口試委員審定書 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv 1 Introduction.................................................... 1 1.1 Outline of the proof............................................. 1 1.2 Structure of the thesis. ........................................... 2 1.3 Acknowledgments ............................................. 2 2 Settings....................................................... 2 2.1 Measures................................................... 2 2.2 Characters.................................................. 3 3 Modular forms .................................................. 4 3.1 Classical modular form........................................... 4 3.2 Modular curves............................................... 6 3.3 q-expansion principle............................................ 9 3.4 Hilbert modular surfaces.......................................... 10 3.5 Toroidal compactifications......................................... 10 4 Serreduality.................................................... 11 4.1 Algebraic curves............................................... 11 4.2 Compact Riemann surfaces ........................................ 12 4.3 Comparison ................................................. 13 4.4 Functoriality................................................. 14 5 Rational Structures................................................ 15 5.1 Generalities ................................................. 15 5.2 Rational Structure from Whittaker model ................................ 15 5.3 Lie algebra cohomology .......................................... 16 5.4 Rational Structure from coherent cohomology ............................. 17 5.5 Periods.................................................... 19 6 Integral representation and cohomological interpretation......................... 19 6.1 Eisenstein series............................................... 19 6.2 Local Asai L-functions ........................................... 22 6.3 Global Asai L-functions; factorization .................................. 23 6.4 Cohomological interpretations ...................................... 26 6.5 Local computation ............................................. 27 6.6 Go to left................................................... 30 Reference ..................................................... 32 | - |
| dc.language.iso | en | - |
| dc.subject | 淺井表現 | zh_TW |
| dc.subject | 週期 | zh_TW |
| dc.subject | 代數性 | zh_TW |
| dc.subject | Rankin-Selberg 積分 | zh_TW |
| dc.subject | 有理結構 | zh_TW |
| dc.subject | algebraicity | en |
| dc.subject | periods | en |
| dc.subject | Rankin-Selberg integrals | en |
| dc.subject | Asai representation | en |
| dc.subject | rational structures | en |
| dc.title | 淺井L函數臨界值的代數性 | zh_TW |
| dc.title | Algebraicity of critical values for Asai L-functions | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 111-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 鄭堯;藍凱文 | zh_TW |
| dc.contributor.oralexamcommittee | Yao Cheng;Kai-Wen Lan | en |
| dc.subject.keyword | 淺井表現,代數性,週期,Rankin-Selberg 積分,有理結構, | zh_TW |
| dc.subject.keyword | Asai representation,algebraicity,periods,Rankin-Selberg integrals,rational structures, | en |
| dc.relation.page | 33 | - |
| dc.identifier.doi | 10.6342/NTU202301138 | - |
| dc.rights.note | 同意授權(限校園內公開) | - |
| dc.date.accepted | 2023-07-11 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 數學系 | - |
| dc.date.embargo-lift | 2028-07-03 | - |
| 顯示於系所單位： | 數學系 | |
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