On the p-adic Riemann hypothesis for the zeta function of divisors
文献类型：期刊论文
| 作者 | Wan, DQ; Haessig, CD |
| 刊名 | JOURNAL OF NUMBER THEORY
 |
| 出版日期 | 2004-02-01 |
| 卷号 | 104期号:2页码:335-352 |
| 关键词 | P-adic Riemann hypothesis zeta function of algebraic cycles zeta function of divisors Riemann-Roch problem effective cone Newton polygon |
| ISSN号 | 0022-314X |
| DOI | 10.1016/j.jnt.2003.08.008 |
| 英文摘要 | In this paper, we continue the investigation of the zeta function of divisors, as introduced by the first author in Wan (in: D. Jungnickel, H. Niederreiter (Eds.), Finite Fields and Applications, Springer, Berlin, 2001, pp. 437-461; Manuscripta Math. 74 (1992) 413), for a projective variety over a finite field. Assuming that the set of effective divisors in the divisor class group forms a finitely generated monoid, then there are four conjectures about this zeta function: p-adic meromorphic continuation, rank and pole relation, p-adic Riemann hypothesis, and simplicity of zeros and poles. This paper proves all four conjectures when the Chow the group of divisors is of rank one. Also, an example with higher rank is provided where all four conjectures hold. (C) 2003 Elsevier Inc. All rights reserved. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000188499300010 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/872]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Wan, DQ |
| 作者单位 | 1.Chinese Acad Sci, Inst Math, Beijing, Peoples R China 2.Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA |
| 推荐引用方式 GB/T 7714 | Wan, DQ,Haessig, CD. On the p-adic Riemann hypothesis for the zeta function of divisors[J]. JOURNAL OF NUMBER THEORY,2004,104(2):335-352. |
| APA | Wan, DQ,&Haessig, CD.(2004).On the p-adic Riemann hypothesis for the zeta function of divisors.JOURNAL OF NUMBER THEORY,104(2),335-352. |
| MLA | Wan, DQ,et al."On the p-adic Riemann hypothesis for the zeta function of divisors".JOURNAL OF NUMBER THEORY 104.2(2004):335-352. |
入库方式： OAI收割
来源：数学与系统科学研究院
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