| 姓名 |
洪昕嵐(Hsin-Lan Hung)
查詢紙本館藏 |
畢業系所 |
數學系 |
| 論文名稱 |
加減法集合的估計以及其運用
(A study of sum-differencesets and its applications)
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| 相關論文 | |
| 檔案 |
 [Endnote RIS 格式]
[Bibtex 格式]
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| 摘要(中) |
在許多經典的加減法數論問題都圍繞在特定的集合上作研究，但在本篇論文裡，我們的重點不是這些類型的問題。相反，我們由一個加法群Z選出非空有限的一般集合A,B，利用一些組合的方法和代數的運算去估計它們的加減法集合，並證明在給定的條件下，集合A可以被集合B的平移所覆蓋。最後我們可將這些基礎數論的方法，運用在討論等差數列集合。 |
| 摘要(英) |
Many classical problems in additive number theory revolve around the study of sum sets for specific sets, in this text, we shall not focus on these types of problems. Instead, we shall focus for more general sets A,B, which are finite and non-empty subsets of an additive group such as Z. We will develop the more elementary theory of sum set estimates. These estimates are obtained by combinatorial considerations, and rely on arithmetic facts. And we prove the lemma which gives conditions under which one set A can be efficiently covered by translates of another set B. In the end, we can use these number- theoretic methods to discuss an arithmetic progression. |
| 關鍵字(中) |
★ 加減法集合的估計
★ 加減法集合的運用 |
關鍵字(英) |
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| 論文目次 |
Abstract(in Chinese) i
Abstract(in English) ii
Contents iii
Notation iv
Introduction 1
Sum set estimates 2
Bounds on arithmetic projections 18
Reference 24 |
| 參考文獻 |
[1] Tao, Terence, and Van H. Vu. Additive Combinatorics Vol. 105. Cambridge University Press, 2006, Ch. 2.
[2] Nets Hawk Katz and Terence Tao. “Bounds on arithemtic projections, and applications to the Kakeya conjecture. “Mathematical Research Letters 6, 625-630(1999). |
| 指導教授 |
沈俊嚴
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審核日期 |
2016-6-15 |
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