活动地点：

活动类型：学术报告

主讲人：Lin Weng

活动时间：

活动内容：

 

Speaker: Professor Lin Weng (Kyushu University) 

Title: Non-Abelian Zeta Functions

Abstract:
Associated to global fields are genuine high rank zeta functions, exposing
non-abelian aspects of the fields. Defined as natural counts over moduli spaces
of stable bundles/lattices, these zetas are canonical as well. For example, when
rank becomes one, they coincide with classical Artin/Dedekind zeta functions for
function fields/number fields. We will talk about their constructions, basic properties,
and related open problems in arithmetic geometry and number theory.

References:
[1] L. Weng, Non-abelian zeta function for function fields, Amer. J. Math. 127 (5) (2005), pp. 973–1017.
[2] L. Weng, Geometric arithmetic: A program, Arithmetic Geometry and Number Theory, Ser. Number Theory Appl. vol. 1, World Sci. Publ., Hackensack, NJ (2006), pp. 211–400.
[3] L. Weng, A rank two zeta and its zeros, J. Ramanujan Math. Soc. 21 (3) (2006), pp. 205–266.
[4] L. Weng, A geometric approach to L-functions, The Conference on L-Functions, World Sci. Publ., Hackensack, NJ (2007), pp. 219–370.
[5] L. Weng, Symmetries and the Riemann Hypothesis, in: Algebraic and Arithmetic Structures of Moduli Spaces, in: Adv. Stud. Pure Math., Math. Soc. Japan, Tokyo, in press.
[6] L. Weng, Zeta functions for Sp(2n), appendix to M. Suzuki"The Riemann hypothesis for Weng's zeta function of Sp(4) over Q", Journal of Number Theory, 129, 2009, 551-579.