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重庆交通大学学报（自然科学版）

重庆交通大学学报（自然科学版） ›› 2011, Vol. 30 ›› Issue (3): 511-513.DOI: 10.3969/j.issn.1674-0696.2011.03.39

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一类二型Fuchsian 群的局部化性质

胡小虎，陈波   

  1. 重庆交通大学理学院，重庆400074
  • 收稿日期:2010-11-15 修回日期:2011-03-10 出版日期:2011-06-15 发布日期:2015-03-12
  • 作者简介:胡小虎(1975—)，男，重庆铜梁人，讲师，硕士，主要从事微分几何与代数方面的研究。E-mail:huxiaohu2008@sina.com。

Local Properties of Some Class of Second Fuchsian Group

HU Xiao-hu，CHEN Bo   

  1. School of Sciences,Chongqing Jiaotong University,Chongqing 400074,China
  • Received:2010-11-15 Revised:2011-03-10 Online:2011-06-15 Published:2015-03-12

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摘要： 为了讨论整数的整二次型表示，引进整二次型的θ－级数，并发现θ－级数与模群的自守形式有紧密的联系。 Fuchsian群及其自守形式是模群与模形式的重要延伸。对于一类二型Fuchsian群H(槡q)，这是G(槡q)的一个子群。 众所周知，G(槡q)中的元素要落H(槡q)中需要有诸多限制。简化这些限制条件是很有意义的。利用p－局部化方 法，首先给出H(槡q)的局部化的性质。然后，给出它与G(槡q)关于模pn的一个关系。

关键词: Fuchsian群, p－进数, 同余子群

Abstract: In order to discuss the representations of an integer by some integral quadric form,theta series of its quadric form was introduced and the close connections between them were found.Fuchsian groups and their automorphic forms were important extensions of modular group and modular forms.For the second Fuchsian group H(槡q) ,it was a subgroups of G (槡q) .It was well known that the elements of G(槡q) which could be in H(槡q) must satisfy many conditions.So it was significant to simplify these conditions.A local property of H( 槡q) was given Byp-adic localization and relation between G (槡q) and H(槡q) by modulo pn was established．

Key words: Fuchsian group, p-adic number, congruence subgroup．

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