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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 謝銘倫 | |
| dc.contributor.author | Yao Cheng | en |
| dc.contributor.author | 鄭堯 | zh_TW |
| dc.date.accessioned | 2021-06-17T05:00:38Z | - |
| dc.date.available | 2018-08-06 | |
| dc.date.copyright | 2018-08-06 | |
| dc.date.issued | 2018 | |
| dc.date.submitted | 2018-07-25 | |
| dc.identifier.citation | [A04] Kable. A. Asai L-functions and Jacquet's conjecture. American Journal of Mathematics, 126(4):789-820, 2004
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Yoshida. Motives and siegel modular forms. American Journal of Mathematics, 123(6):1171-1197, 2001. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/71244 | - |
| dc.description.abstract | 利用Ichino的公式, 我們給了三重積L-函數特殊值的精確公式. 特別的, 我們計算了很多實賦值上的局部周期積分. 關於公式的應用, 我們首先利用這些公式建立三重積L-函數特殊值的代數性. 接著我們利用三重積L-函數特殊值的代數性證明某些GL(2)xGL(3)上自守L-函數中心值的Deligne猜想. | zh_TW |
| dc.description.abstract | We present explicit central value formulae for certain triple product L-functions over a totally real number field by using Ichino's formula. In particular, we carry out explicit computations for the local period integrals at the real defined in the Ichino's formula in very general settings. As applications, we first establish the rationality of the central critical values of these triple product L-functions. Base on this result, we prove the Deligne's conjecture for the central critical values of certain class of automorphic L-functions for GL(2)xGL(3). | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T05:00:38Z (GMT). No. of bitstreams: 1 ntu-107-D02221003-1.pdf: 1366481 bytes, checksum: ebbc29f4be345ed2f89da7d0bb7166dd (MD5) Previous issue date: 2018 | en |
| dc.description.tableofcontents | 口試委員審定書 ……………………………………………………..i
Acknowledgements...………………………………………………...ii 中文摘要 …………………………………………………….............iii Abstract...…………………………………………………………….iv 1. Introduction………………………………………………………..1 1.1. Basic notations…………………………………………………4 2. Local invariant forms……………………………………………...5 2.1. Ichino’s integral………………………………………………...5 2.2. An identity between invariant forms…………………………..5 2.3. Rankin-Selberg integrals……………………………………….7 3. The calculation of local period integrals for matrix algebra: Archimedean case.………………………………………………….9 3.1. Notation and conventions………………………………………9 3.2. Definition of local period integrals……………………………10 3.3. Period integrals for E=R x R x R………………………………14 3.4. Period integrals for E=C x R…..……………………………….22 4. The calculation of local period integrals for matrix algebra: non-Archimedean case……………………………………………..27 4.1. Notation and conventions……………………………………....27 4.2. Definition of period integrals……………………………….….28 4.3. Period integrals for E=F x F x F………………………….……29 4.4. Period integrals for E=F’ x F…………………………………..31 4.5. Period integrals for E is a field……………………….………..34 5. The calculation of local period integrals for division algebra………35 5.1. Notation and conventions……………………………………….35 5.2 Definition of period integrals……………………………………36 5.3. Period integrals for division algebra……………………………38 6. Proof of Proposition 2.3……………………………………………41 6.1. The proof……………………………………………………….41 6.2. Proof of lemma 6.3: Archimedean case………………………..46 6.3. Proof of lemma 6.3: non-Archimedean case…………………...52 6.4. The constant c(delta)……………………………………………57 7. Special value formulae……………………………………………..58 7.1. Notation………………………………………………………...58 7.2. Global settings and assumptions……………………………….58 7.3. Vector-valued automorphic form………………………………59 7.4. Global period integral…………………………………………..60 7.5. The formulae……………………………………………………63 8. Applications………………………………………………………..64 8.1. Modular forms and auromorphic forms………………………..64 8.2. Algebraicity for triple product L-functions……………….66 8.3. Deligne’s conjecture for GL(3) x GL(2)………………………..73 Appendix A: Whittaker functions and matrix coefficients for GL(2)…75 A.1. Notation and convention…………………………………………75 A.2. Whittaker functions for GL(2,C)…………………………………76 A.3. Whittaker functions for GL(2,R)…………………………………77 A.4. Whittaker functions for GL(2,F)…………………………………78 A.5. Matrix coefficients for GL(2,R)……………………………..…80 A.6. Matrix coefficients for GL(2,F)………………………………...81 Appendix B: Description of Kirillov models………………………...83 Appendix C: Root numbers and Deligne’s periods…………………..88 C.1. Root numbers…………………………………………………….88 C.2. Deligne’s period………………………………………………….89 References..…………………………………………………………....90 | |
| dc.language.iso | en | |
| dc.title | 三重積L-函數之特殊值公式及其應用 | zh_TW |
| dc.title | Special value formulae for triple product L-functions and applications | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 106-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 潘戍衍,魏福村,康明軒,K. Namikawa | |
| dc.subject.keyword | 特殊值公式,三重積L-函數,局部周期積分,Ichino公式,Deligne猜想, | zh_TW |
| dc.subject.keyword | Special value formulae,triple product L-functions,local period integrals, | en |
| dc.relation.page | 91 | |
| dc.identifier.doi | 10.6342/NTU201801839 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2018-07-26 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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