Horizontal non-vanishing of Heegner points and toric periods
文献类型：期刊论文
| 作者 | Burungale, Ashay A.2,3; Tian, Ye1,4 |
| 刊名 | ADVANCES IN MATHEMATICS
 |
| 出版日期 | 2020-03-04 |
| 卷号 | 362页码:35 |
| 关键词 | Heegner points Tonic periods Gross-Zagier formula Waldspurger formula |
| ISSN号 | 0001-8708 |
| DOI | 10.1016/j.aim.2019.106938 |
| 英文摘要 | Let F be a totally real number field and A a modular GL(2)-type abelia.n variety over F. Let K/F be a CM quadratic extension. Let x be a class group character over K such that the Rankin-Selberg convolution L(s, A, chi) is self-dual with root number -1. We show that the number of class group characters chi with bounded ramification such that L'(1, A, chi) not equal 0 increases with the absolute value of the discriminant of K. We also consider a rather general rank zero situation. Let pi be a cuspidal cohomological automorphic representation over GL(2)(A(F)). Let chi be a Hecke character over K such that the Rankin-Selberg convolution L(s, pi, chi) is self-dual with root number 1. We show that the number of Hecke characters chi with fixed infinity-type and bounded ramification such that L(1/2, pi, chi) not equal 0 increases with the absolute value of the discriminant of K. The Gross-Zagier formula and the Waldspurger formula relate the question to horizontal non-vanishing of Heegner points and tonic periods, respectively. For both situations, the strategy is geometric relying on the Zariski density of CM points on self-products of a quaternionic Shimura variety. The recent result [26,31,1] on the Andre-Oort conjecture is accordingly fundamental to the approach. (C) 2019 Elsevier Inc. All rights reserved. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000510113300005 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/50807]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Burungale, Ashay A. |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, HLM, MCM, Beijing 100190, Peoples R China 2.Inst Adv Study, Einstein Dr, Princeton, NJ 08540 USA 3.CALTECH, 1200 E Calif Blvd, Pasadena, CA 91125 USA 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 10049, Peoples R China |
| 推荐引用方式 GB/T 7714 | Burungale, Ashay A.,Tian, Ye. Horizontal non-vanishing of Heegner points and toric periods[J]. ADVANCES IN MATHEMATICS,2020,362:35. |
| APA | Burungale, Ashay A.,&Tian, Ye.(2020).Horizontal non-vanishing of Heegner points and toric periods.ADVANCES IN MATHEMATICS,362,35. |
| MLA | Burungale, Ashay A.,et al."Horizontal non-vanishing of Heegner points and toric periods".ADVANCES IN MATHEMATICS 362(2020):35. |
入库方式： OAI收割
来源：数学与系统科学研究院
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