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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 謝銘倫(Ming-Lun Hsieh) | |
| dc.contributor.author | Chung-Ru Lee | en |
| dc.contributor.author | 李宗儒 | zh_TW |
| dc.date.accessioned | 2021-05-13T08:38:16Z | - |
| dc.date.available | 2016-07-25 | |
| dc.date.available | 2021-05-13T08:38:16Z | - |
| dc.date.copyright | 2016-07-25 | |
| dc.date.issued | 2016 | |
| dc.date.submitted | 2016-07-12 | |
| dc.identifier.citation | 1. [BGR84] S. Bosch, U. Güntzer, and R. Remmert, Non-Archimedean analysis, Grundlehren der Mathematischen Wissenschaften[Fundamental Principles of Mathematical Sciences], vol. 261, Springer-Verlag, Berlin, 1984, A systematic approach to rigid analytic geometry. MR 746961
2. [CdS88] Robert Coleman and Ehud de Shalit, p-adic regulators on curves and special values of p-adic L-functions, Invent. Math. 93 (1988), no. 2, 239 266. MR 948100 3. [Col82] Robert F. Coleman, Dilogarithms, regulators and p-adic L-functions, Invent. Math. 69 (1982), no. 2, 171 208. MR 674400 4. [Col85] Robert F. Coleman, Torsion points on curves and p-adic abelian integrals, Ann. of Math. (2) 121 (1985), no. 1, 111 168. MR 782557 5. [Con08] Brian Conrad, Several approaches to non-Archimedean geometry, p-adic geometry, Univ. Lecture Ser., vol. 45, Amer. Math. Soc., Providence, RI, 2008, pp. 9 63. MR 2482345 6. [Kob79] Neal Koblitz, A new proof of certain formulas for p-adic L-functions, Duke Math. J. 46 (1979), no. 2, 455 468. MR 534062 7. [Tat71] John Tate, Rigid analytic spaces, Invent. Math. 12 (1971), 257 289. MR 0306196 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/3902 | - |
| dc.description.abstract | 本文探討在一維p-adic射影空間上的積分理論，並將其使用於建構 p-adic完備域上的對數F-crystal，主要關注在過程中自然構造出的對數多項式函數。對數多項式函數可實際應用在計算p-adic上的L-函數特殊值；準確來說，對數多項式函數在分圓點上的取值和久保田-Leopold L-函數在正整數上的特殊值有連繫。文章以推導Coleman(從Koblitz證明k=1的情形為推廣對象)描述當k為正整數時，L-函數的特殊值以及k次對數多項式關係的公式總結。 | zh_TW |
| dc.description.abstract | In this article we discuss the integration theory on p-adic projective space of dimension 1, and apply it to construct the logarithmic F-crystal on the p-adic complete field, where polylogarithm functions occurs in a natural development. The usage of polylogarithms realize in the computation for the p-adic L-values. To be precise, valuation of the polylogarithms at primitive roots of unity is related to the special values of the Kubota-Leopold L-function at positive integers. Eventually, we conclude by deriving a formula relating the evaluation of p-adic L-functions at k to the k-th polylogarithm, which extends the formula by Koblitz, who proved the case k=1. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-13T08:38:16Z (GMT). No. of bitstreams: 1 ntu-105-R02221030-1.pdf: 7548151 bytes, checksum: 7e051a4b55d62ba84d98906dbd16933e (MD5) Previous issue date: 2016 | en |
| dc.description.tableofcontents | 誌謝 i
中文摘要 ii Abstract iii 口試委員審定書 1. Introduction 1 1.1 Coleman integral in brief 1 1.2 The logarithmic F-crystal and p-adic L-functions 3 2. Rigid Analysis on Punctured p-adic Projective Line 4 2.1 Affinoid subspaces of the p-adic complete field 4 2.2 The logarithm 5 3. The Dwork Principle 6 3.1 Frobenius morphisms 6 3.2 The Dwork Principle 7 4. The Logarithmic F-Crystals 9 4.1 Definition of a logarithmic F-crystal on p-adic affine line 9 4.2 Integration on a logarithmic F-crystal 10 5. Integration Theory for Basic Wide Open Sets 16 5.1 A(U) as a logarithmic F-crystal 16 5.2 The structure of integrated A(U) 17 6. The Polylogarithms 18 6.1 Definition and functional equations of the polylogarithms 18 6.2 The function D(z) and its related identities 20 7. Relation between the Polylogarithms and Special Values of the Kubota-Leopold L-function at Positive Integers 22 7.1 An identity for the valuation of k-th polylogarithm 22 7.2 The p-adic L-function and its special values 23 8. Conclusion and Suggestions 25 References 26 | |
| dc.language.iso | en | |
| dc.subject | 對數多項式 | zh_TW |
| dc.subject | p-adic | zh_TW |
| dc.subject | Coleman積分 | zh_TW |
| dc.subject | L-函數特殊值 | zh_TW |
| dc.subject | 久保田-Leopold L-函數 | zh_TW |
| dc.subject | 對數F-crystal | zh_TW |
| dc.subject | Kubota-Leopold L-function | en |
| dc.subject | special value of L-functions at positive integers | en |
| dc.subject | polylogarithm | en |
| dc.subject | logarithmic F-crystal | en |
| dc.subject | p-adic | en |
| dc.subject | Coleman integral | en |
| dc.title | Coleman積分及p-adic L-函數 | zh_TW |
| dc.title | On Coleman Integration and p-adic L-functions | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳其誠(Ki-Seng Tan),余正道(Jeng-Daw Yu) | |
| dc.subject.keyword | Coleman積分,p-adic,對數F-crystal,對數多項式,久保田-Leopold L-函數,L-函數特殊值, | zh_TW |
| dc.subject.keyword | Coleman integral,p-adic,logarithmic F-crystal,polylogarithm,Kubota-Leopold L-function,special value of L-functions at positive integers, | en |
| dc.relation.page | 26 | |
| dc.identifier.doi | 10.6342/NTU201600789 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2016-07-12 | |
| 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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