傅氏分析在組合學的應用與Roth定理;Applications of finite Fourier analysis to combinations and Roth theorem

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/67652

Title:	傅氏分析在組合學的應用與Roth定理;Applications of finite Fourier analysis to combinations and Roth theorem
Authors:	廖常至;Liao,Chung-Chih
Contributors:	數學系
Keywords:	Roth定理;傅氏分析;組合學;Roth;Fourier analysis;combinations
Date:	2015-06-29
Issue Date:	2015-07-31 01:03:13 (UTC+8)
Publisher:	國立中央大學
Abstract:	Roth 定理闡述了如果一個正整數的子集的"密度"大於0,則它包含一個長度為3的等差數列。在本篇論文,我們探討了傅氏分析在組合學上的一些運用。除此之外,利用一些基本數論的結果,我們了解如何使用傅氏分析來證明Roth 定理。 ;The celebrated result of Roth asserts that there exists an arithmetic progression of length three in a subset in integers with positive upper density. The result has been reproved and generalized later by many people. In this thesis, we study the approaches of Fourier analysis methods. We will see that the Finite Fourier analysis is powerful enough to prove the Roth theorem.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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