GENUS PERIODS, GENUS POINTS AND CONGRUENT NUMBER PROBLEM
文献类型：期刊论文
| 作者 | Tian, Ye1 ; Yuan, Xinyi2; Zhang, Shou-Wu3
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| 刊名 | ASIAN JOURNAL OF MATHEMATICS
 |
| 出版日期 | 2017-08-01 |
| 卷号 | 21期号:4页码:721-774 |
| 关键词 | Congruent number Birch and Swinnerton-Dyer conjecture Tate-Shafarevich group Heegner point Selmer group Gross-Zagier formula Waldspurger formula L-function |
| ISSN号 | 1093-6106 |
| 英文摘要 | In this paper, based on an idea of Tian we establish a new sufficient condition for a positive integer n to be a congruent number in terms of the Legendre symbols for the prime factors of n. Our criterion generalizes previous results of Heegner, Birch-Stephens, Monsky, and Tian, and conjecturally provides a list of positive density of congruent numbers. Our method of proving the criterion is to give formulae for the analytic Tate-Shafarevich number L(n) in terms of the so-called genus periods and genus points. These formulae are derived from the Waldspurger formula and the generalized Gross-Zagier formula of Yuan-Zhang-Zhang. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000408369900005 |
| 出版者 | INT PRESS BOSTON, INC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/26463]  |
| 专题 | 数学所 |
| 通讯作者 | Tian, Ye |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Morningside Ctr Math, Beijing 100190, Peoples R China 2.Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA 3.Princeton Univ, Dept Math, Princeton, NJ 08544 USA |
| 推荐引用方式 GB/T 7714 | Tian, Ye,Yuan, Xinyi,Zhang, Shou-Wu. GENUS PERIODS, GENUS POINTS AND CONGRUENT NUMBER PROBLEM[J]. ASIAN JOURNAL OF MATHEMATICS,2017,21(4):721-774. |
| APA | Tian, Ye,Yuan, Xinyi,&Zhang, Shou-Wu.(2017).GENUS PERIODS, GENUS POINTS AND CONGRUENT NUMBER PROBLEM.ASIAN JOURNAL OF MATHEMATICS,21(4),721-774. |
| MLA | Tian, Ye,et al."GENUS PERIODS, GENUS POINTS AND CONGRUENT NUMBER PROBLEM".ASIAN JOURNAL OF MATHEMATICS 21.4(2017):721-774. |
入库方式： OAI收割
来源：数学与系统科学研究院
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