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Combinatorial zeta and L-functions

李文卿 教授(美国宾夕法尼亚州立大学)
2014年11月10日10:30—11:30  闵行数学楼102报告厅
 
报告人简介:
李文卿教授1970年本科毕业于台湾大学,1974年在加州大学伯克利分校获博士学位。 她现在是美国宾夕法尼亚州立大学数学系的杰出教授,台湾理论科学研究中心主任,美国数学学会资深会员。曾获世界华人数学家大会“陈省身奖”。
她主要从事数论、自守形式、群表示论、组合以及编码等方面的研究,是国际著名的数论专家,她关于模形式理论的研究成果曾被Andrew Wiles在他的著名论文“Fermat's Last Theorem”中引用。

报告内容简介:
Roughly speaking, a zeta function is a counting function. The Selberg zeta function counts closed geodesics in a compact Riemann surface. A combinatorial zeta function is a discrete analogue of the Selberg zeta function. From group theoretical viewpoint, Ihara
generalized the Selberg zeta function from PGL(2) over R to PGL(2) over a p-adic field. Serre realized that Ihara's zeta function can be formulated for all finite graphs.
We studied zeta functions for finite simplicial complexes arising from finite quotients of the building attached to PGL(3) (with Kang) and PGSp(4) (with Fang and Wang) over p-adic fields. Such a zeta function is a rational function with a closed form expression which gives both
topological and spectral information of the underlying combinatorial object. The Artin L-functions for graphs were considered by Ihara, Hashimoto, Stark and Terras, respectively. Very recently in a joint work with Kang we obtained a closed form expression for the Artin L-functions attached to finite quotients of the building of PGL(3).
   
 
 
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