- 學位論文
On Roth's theorem about three-term arithmetic progressions
關於三項等差數列的Roth定理的討論
摘要
In this thesis we will discuss some properties of sets which contain no three-term arithmetic progressions. More precisely, we will discuss some sets without three- terms arithmetic progressions, a key ingredient in Roth's original proof called the Hardy-Littlewood method, and a recent proof of Roth's theorem by Szemeredi.
參考文獻
1. F. A. Behrend, On sets of integers which contain no three terms in arithmetic progression, Proceeding of the National Academy of Sciences, 32 (1946), 331-332
2. J. Bourgain, On triples in arithmetic progression, Geom. Funct. Anal., 9 (1999), 968-984
3. J. Bourgain, Roth's theorem on progressions revisited, Journal D'analyse Mathematique, 104 (2008)
4. J. G. van der Corput, Uber Summen von Primzahlen und Primzahlquadraten, Math. Ann., 116 (1939), 1-50
5. P. Erdos and P. Turan, On some sequences of integers, Journal of the London Mathematical Society, 11 (1936), 261-264
延伸閱讀
- 廖森游（2009）。高中數學三角函數程序試題的研究〔碩士論文，國立臺灣師範大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0021-1610201315150937
- 蔡宗儒（2008）。三維Ostrowski型不等式的研究〔碩士論文，淡江大學〕。華藝線上圖書館。https://doi.org/10.6846/TKU.2008.00085
- 李建勳、邱永興、劉俊槪、涂瑞洪（2006）。三度空間直接線性轉換法誤差之探討。屏東教大體育，(10)，671-684。https://www.airitilibrary.com/Article/Detail?DocID=a0000186-200607-x-10-671-684-a
- Hung, C. L. (2010). 有效率的三條序列演算法及其應用 [doctoral dissertation, National Tsing Hua University]. Airiti Library. https://doi.org/10.6843/NTHU.2010.00685
- 宋懿城（2017）。探討三角函數和差角公式無字證明在教學上的應用〔碩士論文，國立臺灣師範大學〕。華藝線上圖書館。https://doi.org/10.6345/NTNU202202485