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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 謝銘倫(Ming-Lun Hsieh) | |
| dc.contributor.author | Zhi-Lin Zhang | en |
| dc.contributor.author | 張誌麟 | zh_TW |
| dc.date.accessioned | 2023-03-19T23:19:37Z | - |
| dc.date.copyright | 2022-07-05 | |
| dc.date.issued | 2022 | |
| dc.date.submitted | 2022-06-29 | |
| dc.identifier.citation | [Bar78] Daniel Barsky. Fonctions zeta p-adiques d’une classe de rayon des corps denombres totalement réels. In Groupe d’Etude d’Analyse Ultramétrique (5e année: 1977/78), pages Exp. No. 16, 23. Secrétariat Math., Paris, 1978. [BKL18] Alexander Beilinson, Guido Kings, and Andrey Levin. Topological poly-logarithms and p-adic interpolation of L-values of totally real fields. Math.Ann., 371(3-4):1449–1495, 2018. [Bum97] Daniel Bump. Automorphic forms and representations, volume 55 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1997. [Cas73] William Casselman. On some results of Atkin and Lehner. Math. Ann., 201:301–314, 1973. [CD14] Pierre Charollois and Samit Dasgupta. Integral Eisenstein cocycles on GLn, I: Sczech’s cocycle and p-adic L-functions of totally real fields. Camb. J. Math., 2(1):49–90, 2014. [CN79] Pierrette Cassou-Noguès. Valeurs aux entiers négatifs des fonctions zêta et fonctions zêta p-adiques. Invent. Math., 51(1):29–59, 1979. [DD06] Henri Darmon and Samit Dasgupta. Elliptic units for real quadratic fields. Annals of mathematics, pages 301–346, 2006. [Dix03] A. C. Dixon. Summation of a certain Series. Proc. Lond. Math. Soc., 35:284–289, 1903. [DK] Samit Dasgupta and Mahesh Kakde. Brumer-stark units and hilbert’s 12th problem. https://arxiv.org/abs/2103.02516. [DR80] Pierre Deligne and Kenneth A. Ribet. Values of abelian L-functions at negative integers over totally real fields. Invent. Math., 59(3):227–286, 1980. [Hsi12] Ming-Lun Hsieh. On the non-vanishing of Hecke L-values modulo p. Amer. J. Math., 134(6):1503–1539, 2012. [HY21] Ming-Lun Hsieh and Shunsuke Yamana. Restriction of eisenstein series and stark–heegner points. Journal de Théorie des Nombres de Bordeaux, 33(3):887–944, 2021. [Kit94] Koji Kitagawa. On standard p-adic L-functions of families of elliptic cusp forms. In p-adic monodromy and the Birch and Swinnerton-Dyer conjecture (Boston, MA, 1991), volume 165 of Contemp. Math., pages 81–110. Amer. Math. Soc., Providence, RI, 1994. [KL06] Andrew Knightly and Charles Li. Traces of Hecke operators, volume 133 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2006. [Spi14] Michael Spiess. Shintani cocycles and the order of vanishing of p-adic Hecke L-series at s = 0. Math. Ann., 359(1-2):239–265, 2014. 45. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/85608 | - |
| dc.description.abstract | 在 [DD06] 中，作者給出了在 Qp2-{(0,0)} 上的一個p進測度來定義Λ進艾森斯坦模符號，並當p是慣性於F時，通過計算Λ進艾森斯坦模符號在附加於理想類群的閉鏈上的值來構造實二次域F上的p進L函數。我們將此結果推廣到p是分裂於F的情況，並藉由計算艾森斯坦級數的周期積分來獲得p進L函數的插值公式。 | zh_TW |
| dc.description.abstract | In [DD06], the authors proposed a family of p-adic measures on Qp2-{(0,0)} to define the Λ-adic Eisenstein modular symbol, and constructed the p-adic L-function for a real quadratic field F by evaluating the Λ-adic Eisenstein modular symbol at cycles attached to ideal classes of F for p inert in F. We generalize this result to include the case that p is split in F, and to provide explicit interpolation formulae of the p-adic L-function for F by evaluating explicitly the period integral of Eisenstein series over real quadratic fields. | en |
| dc.description.provenance | Made available in DSpace on 2023-03-19T23:19:37Z (GMT). No. of bitstreams: 1 U0001-2706202215052000.pdf: 1046232 bytes, checksum: f2107bb1089fb87e797b40144cbf22df (MD5) Previous issue date: 2022 | en |
| dc.description.tableofcontents | Contents Acknowledgements i Abstract ii 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Notation and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Automorphic Forms and Modular Forms . . . . . . . . . . . . . . . . 7 1.4 Eisenstein Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Period Integral of Eisenstein series 11 2.1 Period integral as a Product of Local Tate Integrals . . . . . . . . . . 11 2.2 Computation of Local Integrals . . . . . . . . . . . . . . . . . . . . . 13 3 Modular Symbol of Eisenstein Series 22 3.1 The Modified Eisenstein Series . . . . . . . . . . . . . . . . . . . . . 22 3.2 Partial Modular Symbols and p-adic Measures . . . . . . . . . . . . . 28 3.3 Period Integral as a Linear Combination of Complex Modular Symbols 31 4 p-adic L-function for Real Quadratic Field 35 4.1 Integration on Xp as a p-adic Modular Symbol . . . . . . . . . . . . . 35 4.2 Construction of the p-adic L-functions . . . . . . . . . . . . . . . . . 41 iii | |
| dc.language.iso | en | |
| dc.subject | 實二次域 | zh_TW |
| dc.subject | 模符號 | zh_TW |
| dc.subject | p-進 | zh_TW |
| dc.subject | L-函數 | zh_TW |
| dc.subject | 實二次域 | zh_TW |
| dc.subject | 艾森斯坦級數 | zh_TW |
| dc.subject | 模符號 | zh_TW |
| dc.subject | p-進 | zh_TW |
| dc.subject | L-函數 | zh_TW |
| dc.subject | 艾森斯坦級數 | zh_TW |
| dc.subject | p-adic | en |
| dc.subject | L-function | en |
| dc.subject | modular symbom | en |
| dc.subject | real quadratic field | en |
| dc.subject | Eisenstein series | en |
| dc.subject | L-function | en |
| dc.subject | p-adic | en |
| dc.subject | modular symbom | en |
| dc.subject | real quadratic field | en |
| dc.subject | Eisenstein series | en |
| dc.title | 實二次域上的p進L函數的模符號構造 | zh_TW |
| dc.title | Modular Symbols Construction of the p-adic L-functions over Real Quadratic Fields | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 110-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 楊一帆(Yi-Fan Yang),陳其誠(Ki-Seng Tan) | |
| dc.subject.keyword | L-函數,p-進,模符號,實二次域,艾森斯坦級數, | zh_TW |
| dc.subject.keyword | L-function,p-adic,modular symbom,real quadratic field,Eisenstein series, | en |
| dc.relation.page | 45 | |
| dc.identifier.doi | 10.6342/NTU202201144 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2022-07-01 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| dc.date.embargo-lift | 2022-07-05 | - |
| 顯示於系所單位： | 數學系 | |
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| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| U0001-2706202215052000.pdf | 1.02 MB | Adobe PDF | 檢視/開啟 |
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