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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳其誠(Ki-Seng Tan) | |
| dc.contributor.author | Jian-Sin Jhu | en |
| dc.contributor.author | 朱建鑫 | zh_TW |
| dc.date.accessioned | 2021-05-13T08:38:52Z | - |
| dc.date.available | 2016-07-06 | |
| dc.date.available | 2021-05-13T08:38:52Z | - |
| dc.date.copyright | 2016-07-06 | |
| dc.date.issued | 2016 | |
| dc.date.submitted | 2016-06-04 | |
| dc.identifier.citation | [1] Cassels J.W.S.Cassels, Rational quadratic forms, Academic Press, London, 1978.
[2] G.L.Watson, Integral quadratic forms, Cambridge University Press, 1960. [3] Jonathan Hanke, local densities and explicit bounds for representatability by a quadratic form, Duke Math. J.124(2004), no 2, 351-388. [4] Jean-Pierre Serre, A course in arithmetic, Graduate Texts in Mathematics 7. Springer-Verlag, New York, 1973. [5] Larry J.Gerstein, Basic quadratic forms, American Mathematical Society, 2008. [6] Manjul Bhargava and Jonathan Hanke, Universal quadratic forms and 290 theorem, Invent. Math.,2005. [7] P. Delign, La conjecture de Weil, I, Inst. Hautes Etudes Sci. Publ. Math. 43(1974), 273-307. MR 0340258. [8] C. L. Siegel, ぴUber die Analytische Theorie der quadratischen Formen. Ann. of Math. 36 (1935), 527–606; Gestammelte Abhandlungen, band I, 1966, pp. 326–405. [9] [Ram16] S. Ramanujan, On the expression of a number in the form ax2 + by2 + cz2 + du2. Proc. Camb. Phil. Soc. 19 (1916), 11?21. [10] Z. I. Borevich and T.R. Shafarevich, Number Thory, Academic Press, 1966. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/3937 | - |
| dc.description.abstract | 這篇文章中，我們研究 Manjul Bhargava 與 Jonathan Hanke 的 290 定理。主要是透過分類一些被稱作上升子的特殊基本二次形，建立起決定任一正定整係數二次形是否為宇態二次形的準則。 | zh_TW |
| dc.description.abstract | In this thesis, we study the 290-theorem of Manjul Bhargava and Jonathan Hanke. Via the classification of certain basic quadratic forms called escalators, we can establish an efficient criterion to determine whether a positive integral quadratic form is universal. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-13T08:38:52Z (GMT). No. of bitstreams: 1 ntu-105-R03221005-1.pdf: 537911 bytes, checksum: d1611676dfc981112df78d23ba4f4cee (MD5) Previous issue date: 2016 | en |
| dc.description.tableofcontents | 1 Introduction 1
2 Notation and setting 3 2.1 The Gram matrix 3 2.2 Integrally equivalence class 4 2.3 The Minkowski-reduced forms 4 2.4 The corresponding lattices 4 3 Escalation 5 4 The Zp-theory 7 4.1 The normalized form 8 4.2 The reduction maps 10 4.2.1 The reduction map of good type 11 4.2.2 The reduction map of zero type 11 4.2.3 The reduction map of bad type 11 4.2.4 The depth 12 4.3 The representability 12 5 The local-global principle 15 5.1 Basic results 15 5.2 The approximation of Zp-forms 16 5.3 The proofs of Theorem 5.3 20 5.4 Example and conclusion 22 6 Analytic method 23 6.1 The theta function associated to 4-dimensional escalators 23 6.2 Fourier coefficients of Eisenstein series E(z) 24 6.3 Fourier coefficients of the cusp form f(z) 30 6.4 The criterion of representability 30 7 Proofs of the main theorems 32 7.1 Summary 32 7.2 The 10-14 switch 32 7.3 The proof of Theorem 1 33 7.4 The proof of Theorem 2 34 8 References 35 | |
| dc.language.iso | en | |
| dc.subject | 表現 | zh_TW |
| dc.subject | 二次形 | zh_TW |
| dc.subject | 整係數 | zh_TW |
| dc.subject | representation | en |
| dc.subject | quadratic forms | en |
| dc.subject | integral-coefficient | en |
| dc.title | 論290-定理 | zh_TW |
| dc.title | On the 290-theorem | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 余正道(Jeng-Daw Yu),謝銘倫(Ming-Lun Hsieh),陳君明(Jun-Ming Chen) | |
| dc.subject.keyword | 二次形,整係數,表現, | zh_TW |
| dc.subject.keyword | quadratic forms,integral-coefficient,representation, | en |
| dc.relation.page | 36 | |
| dc.identifier.doi | 10.6342/NTU201600288 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2016-06-06 | |
| 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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