辛群複體上的ζ函數;Zeta Functions of Complexes Associated to Symplectic Groups

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題名:	辛群複體上的ζ函數;Zeta Functions of Complexes Associated to Symplectic Groups
作者:	王千真
貢獻者:	國立中央大學數學系
關鍵詞:	數學
日期:	2012-12-01
上傳時間:	2014-03-17 14:20:15 (UTC+8)
出版者:	行政院國家科學委員會
摘要:	研究期間：10108~10207;Let F be a nonarchimedean local field. Recently, zeta functions of finite complexes arising from the Bruhat-Tits building associated to the symplectic group Sp4(F) have been introduced by Fang-Li-Wang. They showed that these zeta functions have a closed form expression related to the degree 4 spin L-functions of GSp4(F). The notion of Ramanujan complexes in the symplectic case was also defined in the same paper, with a classification of Ramanujan complexes given in terms of the behavior of zeta functions. In this project, we propose to study the related questions further. Specifically, since there is another important L-functions associated to GSp4(F), known as the degree 5 standard L-function, it is natural to seek for another family of zeta functions for finite complexes arising from the building associated to Sp4(F), which have a closed form expression revealing these degree 5 standard L-functions. Also, as the construction of Ramanujan complexes in the case of GLn involves deep results from representation theory including the Jacquet-Langlands correspondence and Ramanujan conjectures, it would be interesting to understand the nature of Ramanujan complexes, including their existence and explicit construction, in the setting of symplectic groups.
關聯:	財團法人國家實驗研究院科技政策研究與資訊中心
顯示於類別:	[數學系] 研究計畫

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